Answer:
To find out how much Gary's backpack will weigh with the math and science textbooks in it, we need to add the weight of the textbooks to the weight of the backpack:
Total weight = backpack weight + math textbook weight + science textbook weight
Total weight = 1.2 + 3.75 + 2.85
Total weight = 7.8 pounds
Therefore, Gary's backpack will weigh 7.8 pounds with the math and science textbooks in it.
Answer: His backpack will weigh 7.8 pounds
Step-by-step explanation:
Gary's backpack already weights 1.2 pounds without the science and math textbook, now we add the weights of both the math and science textbook.
1.2 + 3.75 = 4.95
4.95 is the weight with only his math textbook in his bag
now we add the science textbooks weight to 4.95
4.95 + 2.85 = 7.8
7.8 is the weight of his backpack with both his science and math textbook in his bag
My question is,
"The midpoint between x and 27 is -3. Find x."
25 points if you get this correct.
Answer:
The number x that is midway between x and 27, and has a midpoint of -3, is -33
midpoint = (x + 27) / 2
We also know that the midpoint is equal to -3, so we can set these two expressions equal to each other and solve for x:
-3 = (x + 27) / 2
Multiplying both sides by 2 gives:
-6 = x + 27
Subtracting 27 from both sides gives:
x = -33
whats 1 5/6 + 1/2
50 ponits
The value of the given expression 1 5/6 + 1/2 = 14/6.
What is improper fraction?A fraction with a numerator higher than or equal to the denominator is said to be inappropriate. A mixed number is transformed into an improper fraction by multiplying the whole number by the fraction's denominator, which is followed by the addition of the numerator. The denominator of the improper fraction changes to reflect the outcome, while the numerator remains the same.
The given expression is 1 5/6 + 1/2.
Convert the mixed fraction into improper fraction:
1 5/6 = (1 x 6 + 5)/6 = 11/6
Thus,
11/6 + 1/2
Take the LCM:
11/6 + 3/6 = 14/6
Hence, the value of the given expression 1 5/6 + 1/2 = 14/6.
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A triangle is equal in area to a rectangle which measures 10cm by 9cm. If the base of the triangle is 12cm long, find its altitude
Answer:
h = 15 cm
Step-by-step explanation:
Area of triangle equals the area of rectangle. As the dimensions of the rectangle is given, we can first find the area of the rectangle.
[tex]\boxed{\bf Area \ of \ the \ rectangle = length * width}[/tex]
= 10 * 9
= 90 cm²
Area of triangle = area of rectangle
= 90 cm²
base of the triangle = b = 12 cm
[tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}bh}[/tex] where h is the altitude and b is the base.
[tex]\bf \dfrac{1}{2} b* h = 90 \\\\\dfrac{1}{2}*12* h = 90[/tex]
[tex]\bf h = \dfrac{90*2}{12}\\\\\boxed{\bf h = 15 \ cm}[/tex]
A local winery wants to create better marketing campaigns for its white wines by understanding its customers better. One of the general beliefs has been that higher proportion of women prefer white wine as compared to men. The company has conducted a research study in its local winery on white wine preference. Of a sample of 400 men, 120 preferred white wine and of a sample of 500 women, 170 preferred white wine. Using a 0.05 level of significance, test this claim.INPUT Statistics required for computation170 = Count of events in sample 1500 = sample 1 size120 = Count of events in Sample 2400 = sample 2 size0.05 = level of significance0 = hypothesized differenceOUTPUT Output valuesSample 1 Proportion 34.00%Sample 2 Proportion 30.00%Proportion Difference 4.00%Z α/2 (One-Tail) 1.645Z α/2 (Two-Tail) 1.960Standard Error 0.031Hypothesized Difference 0.000One-Tail (H0: p1 − p2 ≥ 0)Test Statistics (Z-Test) 1.282p-Value 0.900One-Tail (H0: p1 − p2 ≤ 0)Test Statistics (Z-Test) 1.282p-Value 0.100Two-Tail (H0: p1 − p2 = 0)Test Statistics (Z-Test) 1.276p-Value 0.202Group of answer choicesThis is a one-tail test and the data does support the claim that higher proportion of women prefer white wine as compared to men.This is a one-tail test and the data does not support the claim that higher proportion of women prefer white wine as compared to men.This is a two-tail test and the data does support the claim that higher proportion of women prefer white wine as compared to men.This is a two-tail test and the data does not support the claim that higher proportion of women prefer white wine as compared to men.Question 2. Based on the study results presented in the last question, what is the upper bound for the proportion differences between women and men for a 95% confidence interval?(Note: Please enter a value with 4 digits after the decimal point. For example, if you computed an upper boundary of 23.456% or .23456, you would enter it here in decimal notation and round it to four digits, thus entering .2346).
Answer:
235.65
Step-by-step explanation:
a school stadium contains 2,000 seats. for a certain game, student tickets cost $3 each and nonstudent tickets cost $6 each. what is the least number of nonstudent tickets that must be sold so that the total ticket sales will be at least $8,400 ?
A school stadium contains 2,000 seats. for a certain game, student tickets cost $3 each and nonstudent tickets cost $6 each. it is proved that at least 1,200 non-student tickets must be sold so that the total ticket sales will be at least $8,400.
How do we calculate the number of tickets?Let x be the number of student tickets sold, and y be the number of non-student tickets sold. Then the total ticket sales can be given as follows:Total ticket sales = 3x + 6y As per the given statement, the total ticket sales must be at least $8,400, that is,3x + 6y ≥ 8,400Dividing the above equation by 3, we get, [tex]x + 2y \geq 2,800[/tex]The school stadium contains 2,000 seats, hence the total number of tickets that can be sold is[tex]x + y = 2,000[/tex].Rearranging the above equation, we get, [tex]x = 2,000 - y[/tex]
Substituting this value in the equation [tex]x + 2y \geq 2,800[/tex], we get[tex](2,000 - y) + 2y \geq 2,800[/tex] ⇒ [tex]2,000 + y \geq 2,800[/tex] ⇒[tex]y \geq 800[/tex] Thus, the minimum number of non-student tickets that must be sold so that the total ticket sales will be at least $8,400 is 800. But it has to be more than 800 since only selling 800 non-student tickets is not enough to get at least $8,400. Let's assume that 1,200 non-student tickets are sold.
Now, if 1,200 non-student tickets are sold, then the number of student tickets sold is, [tex]x = 2,000 - y = 2,000 - 1,200 = 800[/tex] Therefore, the total ticket sales can be calculated as follows:Total ticket sales = [tex]3x + 6y= 3(800) + 6(1,200) = 2,400 + 7,200 = 9,600[/tex] Since $9,600 is greater than $8,400, it is proved that at least 1,200 non-student tickets must be sold so that the total ticket sales will be at least $8,400.
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Graph the function f(x)=-(√x+2)+3
State the domain and range of the function.
Determine the vertex and 4 more points.
If you could help me with this, I would really appreciate it. Thank you!
Vertex: The vertex of the function is at the point (-2, 3).
What is domain?The domain of a function is the set of all possible input values (often represented as x) for which the function is defined. In other words, it is the set of all values that can be plugged into a function to get a valid output. The domain can be limited by various factors such as the type of function, restrictions on the input values, or limitations of the real-world scenario being modeled.
What is Range?The range of a function refers to the set of all possible output values (also known as the dependent variable) that the function can produce for each input value (also known as the independent variable) in its domain. In other words, the range is the set of all values that the function can "reach" or "map to" in its output.
In the given question,
Domain: The domain of the function is all real numbers greater than or equal to -2, since the square root of a negative number is not defined in the real number system.
Range: The range of the function is all real numbers less than or equal to 3, since the maximum value of the function occurs at x=-2, where f(x)=3.
Vertex: The vertex of the function is at the point (-2, 3).
Four additional points:When x=-1, f(x)=-(√(-1)+2)+3 = -1, so (-1,-1) is a point on the graph.
When x=0, f(x)=-(√0+2)+3 = 1, so (0,1) is a point on the graph.
When x=1, f(x)=-(√1+2)+3 = 2, so (1,2) is a point on the graph.
When x=4, f(x)=-(√4+2)+3 = -1, so (4,-1) is a point on the graph
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Let sin(2x) = cos(x), where 0° ≤ x < 180°. what are the possible values for x? a. 30° only b. 90° only c. 30° or 150° d. 30°, 90°, or 150°
If sin(2x) = cos(x), where 0° ≤ x < 180°, then, The possible angle values of x are 90°, 30° and 150°.
The sine and the cosine are trigonometric functions of the angles. The sine and cosine of an acute angle are defined in the context of a right triangle: for a given angle, its sine is the ratio of the length of the side opposite the angle to the length of the longest side of the angle. triangle (the hypotenuse ), and the cosine is the adjacent side The ratio of the length to the hypotenuse.
According to the Question:
Given that,
sin(2x) = cos(x) where 0° ≤ x < 180°
We know that:
sin(2x) = 2 sin(x) cos(x)
⇒ 2 sin(x) cos(x) = cos(x)
Subtract cos(x) on both sides
2 sin(x) cos(x) - cos(x) = 0
cos(x) (2sinx-1)=0
It means, cos(x) = 0 and (2sin x -1 ) = 0
cos x = cos0 and sinx(x) = 1/2
x = 90° and x = 30°, 150°
Hence, the possible values of x are 90°, 30° and 150°.
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What is an equation for the quadratic function represented by the table shown?
In the month of August, your electric bill was $145. 68. What is the hourly cost of electricity in your home?
The hourly cost of electricity in your home is $0.20
So, if we divide your $145.68 electric bill by the number of kilowatt-hours used in that month, we can determine the cost per kilowatt-hour.
If you used 500 kWh in the month of August, your cost per kWh would be $0.29136 ($145.68 / 500 kWh).
If you used 500 kWh in August, your average power usage would be approximately 0.69 kW (500 kWh / 720 hours).
To calculate the hourly cost of electricity, simply multiply the average power usage in kW by the cost per kWh.
Then, the hourly cost of electricity would be approximately $0.20 ($0.29136 * 0.69 kW).
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The polynomial function A(t) = 0.003631 +0.03746t? +0.10121 + 0.009 gives the approximate blood alcohol concentration in a 170-lb woman t hours after drinking 2 oz of alcohol on an empty stomach, fort in the interval [0,5). a. Approximate the change in alcohol level from 3 to 3.2 hours. b. Approximate the change in alcohol level from 4 to 4.2 hours. a. Let y = A(t). Which expression correctly approximates the change in alcohol level from 3 to 3.2 hours? O A. 0.2A (3) OB. 0.2A (3.2) OC. A'(3) OD. A'(3.2) l. The approximate change in alcohol level from 3 to 3.2 hours is (Round to three decimal places as needed.) . b. The approximate change in alcohol level from 4 to 4.2 hours is (Round to three decimal places as needed.)
a. To approximate the change in alcohol level from 3 to 3.2 hours and the correct expression is OC: A'(3).
For this we need to calculate the difference between the values of A(t) at t = 3.2 and t = 3. The expression that correctly approximates this change is given by: A'(3) * 0.2, where A'(t) is the derivative of A(t) with respect to t. Therefore, the correct expression is OC: A'(3).
b. Similarly, to approximate the change in alcohol level from 4 to 4.2 hours, we need to calculate the difference between the values of A(t) at t = 4.2 and t = 4. The expression that correctly approximates this change is again given by: A'(4) * 0.2. Therefore, the correct expression is also OC: A'(4).
To calculate the approximate changes in alcohol level, we need to find the derivative of A(t) with respect to t:
A'(t) = 0.03746 + 0.20242t
a. The approximate change in alcohol level from 3 to 3.2 hours is:
A'(3) * 0.2 = (0.03746 + 0.20242(3)) * 0.2 ≈ 0.118
Therefore, the approximate change in alcohol level from 3 to 3.2 hours is 0.118.
b. The approximate change in alcohol level from 4 to 4.2 hours is:
A'(4) * 0.2 = (0.03746 + 0.20242(4)) * 0.2 ≈ 0.149
Therefore, the approximate change in alcohol level from 4 to 4.2 hours is 0.149.
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Data were recorded for a car's fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour
(mph). Given the least-squares regression line, In(Fuel Efficiency) = 1.437 + 0.541 In(Speed), what is the predicted fuel
efficiency for a speed of 30 mph?
17.67 mpg
26.50 mpg
30.00 mpg
37.74 mpg
The predicted fuel efficiency for a speed of 30 miles per hour is given as follows:
26.50 mpg.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is defined as follows:
In(Fuel Efficiency) = 1.437 + 0.541 In(Speed).
The speed is of 30 miles per hour, hence the predicted fuel efficiency is given as follows:
In(Fuel Efficiency) = 1.437 + 0.541 x In(30).
In(Fuel Efficiency) = 3.277.
The exponential is the inverse of the ln, hence:
Fuel Efficiency = e^3.277
Fuel Efficiency = 26.50 mpg.
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James have 18 litres of water. He poured unequally into 3 tank
I. Poured three quarter of water from tank one into tank 2
II. Poured half of the water that is now in tank 2 into tank 3
III. Poured one third of water that is now in tank 3 into tank 1
Find how much water is in each tanks
Answer:
ames have 18 litres of water. He poured unequally into 3 tank
I. Poured three quarter of water from tank one into tank 2
II. Poured half of the water that is now in tank 2 into tank 3
III. Poured one third of water that is now in tank 3 into tank 1
Find how much water is in each tanks
Step-by-step explanation:
Let's start with the amount of water in tank 1 as x liters.
I. Poured three quarter of water from tank one into tank 2, so tank 1 now has 1/4 of x liters and tank 2 has 3/4 of x liters.
II. Poured half of the water that is now in tank 2 into tank 3, so tank 2 now has 3/8 of x liters and tank 3 has 3/8 of x liters.
III. Poured one third of water that is now in tank 3 into tank 1, so tank 3 now has 1/3 * 3/8 * x = 1/8 * x liters and tank 1 has 1/4 * x + 1/8 * x = 3/8 * x liters.
We know that James poured 18 liters of water into the three tanks, so the sum of the water in the three tanks must be 18 liters.
3/8 * x + 3/8 * x + 1/8 * x = 18
Simplifying the equation, we get:
7/8 * x = 18
x = 18 * 8 / 7 = 20.57 (rounded to two decimal places)
Therefore, the amount of water in each tank is:
Tank 1: 3/8 * x = 7.71 liters
Tank 2: 3/8 * x = 7.71 liters
Tank 3: 1/8 * x = 2.57 liters
state the null hypothesis and alternative hypothesis, in notation, for the individual t-test for testing the slope coefficient associated with?
The null hypothesis and alternative hypothesis in the notation for the individual t-test for testing the slope coefficient associated with a simple linear regression are given below:
Null hypothesis: H₀: β₁ = 0
Alternative hypothesis: Hₐ : β₁ ≠ 0
The hypothesis test is used to determine whether or not there is sufficient evidence to support the alternative hypothesis that the slope of the regression line is not equal to zero. The null hypothesis is that the slope of the regression line is equal to zero.
Therefore, we will use the individual t-test for the slope coefficient to test the hypothesis regarding the slope of the regression line. The formula for the t-test for the slope coefficient is given below:
t = (b₁– β₁) / SEb₁
Where b₁ is the sample slope coefficient β₁ is the hypothesized value of the slope coefficient (i.e., 0) SEb₁ is the standard error of the slope coefficient.
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Hollie takes out a loan of £800. This debt increases by 26% every year. How much will Hollie owe in 13 years?
The amount of owing that Hollie in 13 years will be £3739.68.
We know that the compound interest is given as
A = P(1 + r)ⁿ
A = £800[tex](1 + 0.26)^{13}[/tex]
Simplify the equation, then we have
A = £800 x [tex](1 + 0.26)^{13}[/tex]
A = £800 x [tex]1.26^{13}[/tex]
A = 800 × 4.6746
A = 3739.68
Compound interest refers to the interest earned not only on the principal amount of a loan or investment but also on any accumulated interest that has been added to it over time. In other words, the interest is calculated on both the initial amount of money borrowed or invested, as well as on the interest that has accrued on that amount.
This means that as time goes on, the interest earned on an investment or loan can grow exponentially, as the interest earned in previous periods is included in the calculation for future periods. This compounding effect can result in significant growth over long periods of time. compound interest is an essential concept in finance and can have a significant impact on the growth of investments over time.
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Which of the following are negative integers? Select all that are correct
A the sum of two positive integers
B. The sum of two negative integers
C different of a positive integer that is greater than it
D the difference of a negative integer and an integer and an integer that is greater than it but that is not its opposite
Answer:
B. The sum of two negative integers
Cage different of a positive integer that is greater than it
Step-by-step explanation:
I don't get it, if it means this -(-7) then is not negative
if it this -9-7 then it's correct
hope it helps
Can anyone solve this problem please? Thanks!
The trapezoid has a surface area of 480 square units.
What is the measurement for a trapezoid's area?So, a trapezoid measured in feet offers an area in square feet; one measured in millimetres gives an area in square centimetres; and so on. If it's simpler for you, you can add the lengths of the bases and then divide the total by two. Keep in mind that multiplication by 12 is equivalent to dividing by 2.
We must apply the formula for a trapezoid's area to this issue in order to find a solution:
[tex]A = (1/2) * (a + b) * h[/tex]
where h is the trapezoid's height (or altitude) and a and b are the lengths of its parallel sides.
The values for a, b, and h are provided to us, allowing us to change them in the formula:
A = (1/2) * (20 + 60) * 12
A = (1/2) * 80 * 12
A = 480 square units
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an amusement park charges a $ entrance fee. it then charges an additional $ per ride. which of the following equations could bum so use to properly calculate the dollar cost, , of entering the park and enjoying rides?
The equation you would use to properly calculate the dollar cost of entering the park and enjoying rides is Total Cost = Entrance Fee + (Number of Rides x Ride Fee).
In this case, Total Cost is the cost of entering the park and enjoying rides, Entrance Fee is the fee for entering the park, Number of Rides is the number of rides you will be taking, and Ride Fee is the fee charged for each ride.
Thus, plugging in the given values, the equation becomes Total Cost = Entrance Fee + (Number of Rides x Ride Fee).
Therefore, if the Entrance Fee is $ and each ride costs an additional $ , the Total Cost of entering the park and enjoying rides is $ .
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the area of rectangle is 297 sq cm if its length is increased by 3 cm and width decreases by 1 cm its area increased by 3 cm. sq. find the length and width of rectangle
The length and width of the rectangle are 12.5 cm and 22 cm, respectively.
Let L be the length of the rectangle, and W be the width of the rectangle, then we have that:
L x W = 297 sq cm 1.
If the length is increased by 3 cm and width decreased by 1 cm, then we have that:
(L + 3) x (W - 1) = 297 + 3 sq cm -......(2).
Expand equation 2, we have:
LW + 2L - W = 300 sq cm-.......(3)
We have two equations from 1 and 3:
LW = 297 sq cm LW + 2L - W = 300 sq cm 3.
Substitute equation 1 into equation 3.
297 + 2L - W = 300 sq cm
2L - W = 3 sq cm
2L - W = 3 sq cm
2L = W + 3 sq cm
L = (W + 3)/2 sq cm
W x (W + 3)/2 = 297 sq cm
W² + 3W - 594 = 0 (W + 27) (W - 22) = 0
Therefore, the width of the rectangle is either 22 cm or -27 cm. Since the width cannot be negative, we discard the value of -27 cm. Therefore, the width of the rectangle is 22 cm. Finally, let's calculate the length of the rectangle:
L = (W + 3)/2 sq cm L = (22 + 3)/2 sq cm L = 25/2 sq cm L = 12.5 sq cm
Therefore, the length and width of the rectangle are 12.5 cm and 22 cm, respectively.
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You are sitting in a classroom next to the wall looking at the blackboard at the front of the room. The blackboard is 12 ft
long and starts 3 ft from the wall you are sitting next to. Show that your viewing angle is
a=cot^-1 x/15 - cot^-1 x/3
if you are a ft from the front wall.
The viewing angle a of a person sitting a distance x from the front wall of a classroom with a blackboard that is 12 ft long and starts 3 ft from the wall they are sitting next to can be calculated as: a = cot-1(x/15) - cot-1(x/3)
To understand this calculation, let's consider a diagram of the classroom.
We can see from the diagram that the blackboard has length 12 ft, starting 3 ft from the wall the student is sitting next to. The student is sitting a distance x from the front wall.
The viewing angle a is the angle between the wall the student is sitting next to and the line from the student to the front wall. This angle can be calculated using the tangent of the opposite side (front wall) and adjacent side (wall the student is sitting next to).
We can therefore write: a = tan-1(12/3) - tan-1(x/3)
Simplifying this equation, we can rewrite it as: a = cot-1(x/15) - cot-1(x/3).
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what is the x? please help its very important
Which of the following represents the graph of f(x) = one half to the power of x ? (1 point)
Group of answer choices
graph begins in the second quadrant near the axis. Graph increases slowly while crossing the ordered pair 0, 1. The graph then begins to increase quickly throughout the first quadrant.
graph begins in the second quadrant and decreases quickly while crossing the ordered pair 0, 1. The graph then begins to decrease slowly as it approaches the x axis.
graph begins in the second quadrant and decreases quickly while crossing the ordered pair 0, 3. The graph then begins to decrease slowly as it approaches the line y equals 2.
graph begins in the second quadrant and increases quickly while crossing the ordered pair 0, 3. The graph then begins to increase quickly throughout the first quadrant.
The graph of f(x) = one half to the power of x is:
graph begins in the second quadrant and decreases quickly while crossing the ordered pair (0, 1). The graph then begins to decrease slowly as it approaches the x axis.
How to find the graphThe graph of f(x) = one half to the power of x is an exponential function with a base of one half.
This is written in equation form as
f(x) = (1/2)^x
As x increases, the value of the function decreases exponentially, but the rate of decrease slows down as x approaches positive infinity.
When x is zero, the value of the function is 1, and as x increases, the value of the function decreases slowly.
The graph is attached
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find the area and circumference of the circle below.round your answers to the nearest hundredth
Answer:
Step-by-step explanation:
The area of given circle is 28.27 sq.m. The circumference of given circle is 18.85 m (rounded to the nearest hundredth).
Give a short note on Circumference?The circumference of a circle is the distance around the edge or boundary of the circle. It is also the perimeter of the circle. The circumference is calculated using the formula:
C = 2πr
where "C" is the circumference, "π" is a mathematical constant approximately equal to 3.14159, and "r" is the radius of the circle.
The circumference of a circle is proportional to its diameter, which is the distance across the circle passing through its center. Specifically, the circumference is equal to the diameter multiplied by π, or:
C = πd
where "d" is the diameter of the circle.
Given that the diameter of the circle is 6m.
We know that the radius (r) of the circle is half of the diameter (d), so:
r = d/2 = 6/2 = 3m
The area (A) of the circle is given by the formula:
A = πr²
Substituting the value of r, we get:
A = π(3)² = 9π ≈ 28.27 sq.m (rounded to the nearest hundredth)
The circumference (C) of the circle is given by the formula:
C = 2πr
Substituting the value of r, we get:
C = 2π(3) = 6π ≈ 18.85 m (rounded to the nearest hundredth)
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The complete question is:
Solve the simultaneous equations below using substitution.
y=10x+6
2y+5x=17
Give your answers as integers or decimals.
Therefore, the solution to the system of equations is: x = 1/5 and y = 8.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. Equations contain variables, which are symbols that represent unknown or varying quantities, and constants, which are known values. The variables and constants are connected by mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and the resulting expression on both sides of the equation must have the same value. Equations are used to solve problems, find unknowns, and express relationships between quantities. Some common types of equations include linear equations, quadratic equations, polynomial equations, exponential equations, and trigonometric equations.
Here,
We have the following system of equations:
y = 10x + 6
2y + 5x = 17
Using substitution method, we can substitute the expression for y in the second equation with the expression for y in the first equation:
2(10x + 6) + 5x = 17
Simplifying:
20x + 12 + 5x = 17
25x = 5
x = 5/25 = 1/5
Now we can substitute this value of x into either of the two original equations to find the corresponding value of y. Using the first equation:
y = 10(1/5) + 6
y = 2 + 6
y = 8
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Mabel read a total of 340 pages over 20 hours. In all, how many hours of reading will Mabel have to do this week in order to have read a total of 476 pages? Solve using unit rates
Mabel will have to read for a total of 28 hours to have read a total of 476 pages.
To solve this problem using unit rates, we can start by finding the rate at which Mabel reads in pages per hour. This can be calculated by dividing the total number of pages she read by the total number of hours she spent reading:
Rate = Total pages / Total hours
Rate = 340 / 20
Rate = 17 pages per hour
This means that Mabel reads at a rate of 17 pages per hour. To find out how many hours of reading she will have to do to reach a total of 476 pages, we can use the unit rate to set up a proportion:
17 pages / 1 hour = 476 pages / x hours
Simplifying the proportion by cross-multiplying:
17x = 476
Dividing both sides by 17:
x = 28
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Find the volume and surface area of soda if the radius is 6cm and the height is 11cm
The soda can has an estimated volume of 1,026.72 cubic centimeters and an estimated surface area of 452.39 square centimeters.
To find the volume and surface area of a soda can with radius 6 cm and height 11 cm, we can use the formulas:
Volume of cylinder = πr²h
Surface area of cylinder = 2πrh + 2πr²
Substituting the given values, we get:
Volume = π × 6² × 11
Volume = 1,026.72 cubic centimeters (rounded to two decimal places)
Surface area = 2π × 6 × 11 + 2π × 6²
Surface area = 452.39 square centimeters (rounded to two decimal places)
Therefore, the volume of the soda can is approximately 1,026.72 cubic centimeters, and the surface area is approximately 452.39 square centimeters.
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A savings account pays a 3% nominal annual interest rate and has a balance of $1,000. Any interest earned is deposited into the account and no further deposits or withdrawals are made. If interest is compounded semi-annually (every six months), what interest rate would be used for each calculation?
A. 3%
B. 2%
C. 1.5%
D. 12%
E. 18%
The answer is: C. 1.5%
HELPPPP HURRY PLSS………………..
Answer:
C is your answer
Step-by-step explanation:
in my opinion, i think it would be the mode.
Mo spends £20 on ingredients to make 50 cookies.
He sells all 50 cookies for 56p each.
Work out Mo’s percentage profit.
Look at the circle graph showing the pet ownership data.
Pet Ownership
5%
6%
30%
4%
55%
Dogs
Cats
Fish
Rabbits
Hamsters
If 35 rabbits are owned, how many hamsters are owned? Enter the answer in the box.
The number of hamsters owned according to the circle graph is 28.
What is a pie-chart?A pie chart is a visual representation of data that looks like a pie with the slices representing the size of the data. To show data as a pie chart, a list of numerical variables and category variables are required. Each slice in a pie chart has an arc that is proportionate to the quantity it depicts, and as a result, the area and center angle it generates are also proportional.
Let us suppose the total number of animals = x.
Given that, a total of 35 rabbits are owned.
Thus,
5% of x = 35
5/100 (x) = 35
x = 35(100)/5
x = 700
Now, there are 4% hamsters, thus:
4% of 700 = number of hamsters.
H = 4/100 (700)
H = 28
Hence, the number of hamsters owned according to the circle graph is 28.
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A box contains 4 bags of sugar. The mass of each bag is 6 kilograms. What is the total mass of the box in grams?
[tex]\bold{Solution:}[/tex]
[tex]\text{Total number of Bags} = 4[/tex]
[tex]\text{Total mass in 4 bags } = 6 \ \text{kg}[/tex]
[tex]\text{Total mass in 1 bag}}=\dfrac{6}{4} \ \text{kg}[/tex]
[tex]\bold{We \ know \ that}[/tex]
[tex]\text{1 kg = 1000 gram}[/tex]
[tex]\text{1 gm}= \dfrac{1}{1000} \ \text{kg}[/tex]
[tex]\text{we have to convert} \ \dfrac{6}{4} \ \text{kg to grams}[/tex]
[tex]\dfrac{6}{4} \ \text{kg} = \dfrac{6}{4} \times 1000 \ \text{gm}[/tex]
[tex]=1750 \ \text{gm}[/tex]
[tex]\bold{So, \ the \ total \ mass \ of \ the \ box \ in \ grams \ is \ 1,500 \ gm}[/tex]