The values of a and b of the exponential function are 10000 and 0.6 respectively
How to solve exponential functions?We are given that the exponential function is expressed in general form as; f(x) = abˣ
where;
a is a non-zero real number called the initial value
b is any positive real number such that
b ≠ 1.
The domain of f is all real numbers.
The range of f is all positive real numbers if a > 0.
The range of f is all negative real numbers if a < 0.
The y-intercept is (0, a)
The horizontal asymptote is; y = 0.
We are told that this exponential function passes through the coordinate points (0, 10000) and (3, 2160).
At coordinate point (0, 10000), we have;
10000 = ab⁰
a = 10000
Now, at the coordinate point (3, 2160), we have;
2160 = 10000(b)³
2160/10000 = b³
0.216 = b³
b = ∛0.216
b = 0.6
Thus, we can conclude that the values of a and b of the given exponential function are respectively 10000 and 0.6.
Read more about Exponential Functions at; https://brainly.com/question/11464095
#SPJ1
A jewlary shop sells 240 necklaces in a month 180 of the necklaces were sold in a via the shops website the rest were sold in a high street shop .
Work out the ratio of online sales to shop sales
Give ur answers in its simplest form
A triangle has sides with lengths of 3 miles, 4 miles, and 6 miles. Is it a right triangle
Yes, the given triangle is a right triangle.
We have,
This can be determined by applying the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Now,
In this case, the squares of the side lengths are:
3² = 9
4² = 16
6² = 36
If the sum of the squares of the two shorter sides (9 + 16 = 25) is equal to the square of the longest side (36), then the triangle is a right triangle.
Thus,
In this case, since 25 is indeed equal to 36, the triangle with side lengths 3 miles, 4 miles, and 6 miles is a right triangle.
Learn more about triangles here:
https://brainly.com/question/25950519
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ1
5. (6 pts pts) The displacement of a spring vibrating in damped harmonic motion is given by
y = 4e-3t sin(2πt)
Find the times when the spring is at its equilibrium position (y = 0). '
The times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.
To find the times when the spring is at its equilibrium position (y = 0), we can set the displacement equation equal to zero and solve for t:
[tex]4e^{(-3t)[/tex] sin(2πt) = 0
Since the product of two factors is zero if and only if at least one of the factors is zero, we have two cases to consider:
4[tex]e^{(-3t)[/tex] = 0
This equation has no solution since [tex]e^{(-3t)[/tex] is always positive and nonzero.
sin(2πt) = 0
The sine function is zero at integer multiples of π.
So, we can set 2πt equal to integer multiples of π:
2πt = 0, π, 2π, 3π, ...
Solving for t in each case, we get:
t = 0, 1/2, 1, 3/2, ...
Therefore, the times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.
Learn more about Integral Multiple here:
https://brainly.com/question/30156681
#SPJ1
Help me with this problem please.
The product of matrices A and B are:
[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]
[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]
How to find the product of two matrices?A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.
The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.
The product of matrices A and B are:
AB = A * B
[tex]AB = \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right] * \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right][/tex]
To get the product, multiply each row by the column. That is:
(-3 * 6) + (-8 * 4) = -50
(-3 * 3) + (-8 * (-2)) = 7
(2 * 6) + (8 * 4) = 44
(2 * 3) + (8 * (-2)) = -10
[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]
BA = B * A
[tex]BA = \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right] * \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right][/tex]
To get the product, multiply each row by the column. That is:
(6 * (-3)) + (3 * 2) = -12
(6 * (-8)) + (3 * 8) = -30
(4 * (-3)) + ((-2) * 2) = -16
(4 * (-8)) + ((-2) * 8) = -48
[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]
Learn more about matrices on:
brainly.com/question/11989522
#SPJ1
I need help finding the Component form and Magnitude of the vector V.
To find the magnitude of the vector, we can use the Pythagorean theorem: ||V|| = sqrt((5 * √2 / 2)^2 + (5 * √2 / 2)^2) = 5.
To find the component form of a vector, you need to break it down into its x and y components. Let's say our vector V has a magnitude of 5 and is pointing in the direction of 45 degrees (measured from the positive x-axis).
To find its x component, we can use cosine: Vx = V cos(45) = 5 * √2 / 2. To find its y component, we can use sine: Vy = V sin(45) = 5 * √2 / 2. So the component form of vector V is (5 * √2 / 2, 5 * √2 / 2).
To learn more about : vector
https://brainly.com/question/15519257
#SPJ11
if x+y+z=27 and x+y=17 then Z=
Answer:
Step-by-step explanation:
x+y+z=27
x+y=17
z=?
since x+y=17
then
17+z=27
z=27-17
z=10
A rectangular prism measures 8 inches in width, 12 inches in length, and 4 inches in height. What is the surface area of the prism?
Step-by-step explanation:
It has
two sides 8x12
two sides 12x4
two sides 4x8 total 352 in^2
f(x) = x²/x² 2x+3 find Vertical asymptote find horizontal asymptote
The vertical asymptote of the equation does not exist, the horizontal asymptote of the equation is 1.
To calculate vertical asymptote,
Putting the denominator equal to zero,
x²+2x+3 = 0
Using Quadratic formulae,
b² - 4ac
where,
b = 2
a = 1
c = 3
putting value,
4-12 = -8<0
therefore, the solution is negative
Hence, no vertical asymptote of the given equation exists,
To calculate the horizontal asymptote,
the degrees of the numerator and denominator are the same. we can compare the coefficients of the highest power terms.
The coefficient of x² in the numerator is 1
Hence, the horizontal asymptote is y = 1.
To learn more about asymptotes, here:
https://brainly.com/question/32503997
#SPJ1
A given triangle has vertices at (-3, 1) (2, 4) and (5, -3). If the triangle were rotated 360 degrees clockwise, the new coordinates would be:
At a conference of educators, there ore 189 people total, and 128 are teachers. If the rest are principals, then how many principals are present?
Answer:
61 principals
Step-by-step explanation:
189 total - 128 teachers = 61 principals
Help me solve this problem please
Answer:
450°
Step-by-step explanation:
find the perimeter of a rectangle if: L= 12cm, W= 5cm.
(a) 34cm
(b) 21cm
(c) 14cm
(d) 17cm
Answer:
(a) 34 cm
Step-by-step explanation:
The formula for perimeter of a rectangle is
P = 2l + 2w, where
P is the perimeter,l is the length,and w is the width.Thus, we can plug in 12 for l and 5 for w in the perimeter formula and simplify to find the perimeter of the rectangle:
P = 2(12) + 2(5)
P = 24 + 10
P = 34
Thus, the perimeter of a rectangle with a length of 12 cm and a width of 5 cm is 34 cm.
Find the exact values of the six trigonometric functions of the angle O shown in the figure.
sin(0) -
X
cos(0) -
tan(0) -
csc(0) -
sec(0)-
cot(0) -
0
3
3
The values of
1. cosθ = √3/2
2. sinθ = √3/2
3. tanθ = 1
4. sec θ = 2/√3
5. cosec θ = 2/√3
6. cot θ = 1
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
cosθ = adj/hyp
sinθ = opp/hyp
tanθ = opp/adj
sec θ = 1/cosθ
cosec θ = 1/sinθ
cot θ = 1/tanθ
We need to find the hypotenuse of the triangle
x² = 3² +3²
x = √9+9
x = √18
x = 2√3
cosθ = 3/2√3 = 6√3/12
= √3/2
2. sinθ = 3/2√3 = √3/2
3. tanθ = 3/3 = 1
4. sec θ = 2/√3
5. cosec θ = 2/√3
6. cot θ = 1
learn more about trigonometric ratio from
https://brainly.com/question/24349828
#SPJ1
Using the given scale 1:50, calculate the actual length of the wall if it is measured to be 15cm.
A dentist was making note of her upcoming appointments with different aged patients and
the reasons for their visits.
Patients under 18
Patients 19-60
Patients over 60
Regular cleaning Broken tooth
Submit
5
3
3
2
6
2
What is the probability that a randomly selected appointment is not with a patient 19-60 or is
not for a broken tooth?
Simplify any fractions.
Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (5/21)
The probability of an event is calculated as the number of elements in that event divided by the total number of elements in the sample space.
For this question, we are told to find the probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning.
Number of patients that are over 60 years and are for regular cleaning = 10
Total number of patients = 2 + 8 + 6 + 4 + 10 + 12 = 42
Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (10/42)
= (5/21)
Learn more about the probability visit:
https://brainly.com/question/13604758
#SPJ1
Volume of Cone ___ mm3?
The volume of the cone is 301. 44mm³
How to determine the valueFirst, we need to know the formula
the formula that is used for calculating the volume of a cone is expressed as;
V = πr²h/3
Such that the parameters are;
V is the volume r is the radiush is the height of the coneSubstitute the values, we have;
Volume = 3.14 × 6² × 8/3
Multiply the values, we have;
Volume = 904.32/3
Divide the values
Volume = 301. 44mm³
Learn more about volume at: https://brainly.com/question/1972490
#SPJ1
Use the given data to make a box-and-whisker plot.
5, 4, 16, 21, 10, 6, 15
Answer:
To make a box-and-whisker plot, we first need to order the data from smallest to largest:
4, 5, 6, 10, 15, 16, 21
Next, we can find the median, which is the middle value of the ordered data set. In this case, the median is 10.
Then, we can find the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set. To find Q1 and Q3, we can split the data set into two halves:
4, 5, 6, 10 and 15, 16, 21
The median of the lower half is (5+6)/2 = 5.5, and the median of the upper half is (16+21)/2 = 18.5. Therefore, Q1 = 5.5 and Q3 = 18.5.
Now we can draw the box-and-whisker plot. The box represents the middle 50% of the data, with the bottom of the box at Q1 (5.5), the top of the box at Q3 (18.5), and the line inside the box at the median (10). The whiskers extend from the box to the smallest and largest values inthe data set that are not outliers. To determine whether there are outliers, we can use the following formula:
Outlier = Q1 - 1.5 * (Q3 - Q1) or Q3 + 1.5 * (Q3 - Q1)
Plugging in the values, we get:
Outlier = 5.5 - 1.5 * (18.5 - 5.5) = -13.25 or Outlier = 18.5 + 1.5 * (18.5 - 5.5) = 37.25
Since there are no values in the data set that are less than -13.25 or greater than 37.25, there are no outliers.
Therefore, the box-and-whisker plot for the given data is:
| 4
___|___
| |
| |
| 5.5 |-----
| | |
| | |
|------------| 10 |
| | |
| 15.5 |------
| | |
___|___
| 21
The box spans from Q1 (5.5) to Q3 (18.5), with the median line inside the box at 10. The whiskers extend from the box to the minimum value of 4 and the maximum value of 21, since there are no outliers.
Hope this helps!
With a short time remaining in the day, a delivery driver has time to make deliveries at seven locations among the 8 locations remaining. How many different routes are possible? Question content area bottom Part 1 There are enter your response here possible different routes. (Simplify your answer.)
The number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.
The number of different routes possible for the delivery driver can be calculated using combinatorics. Specifically, we need to determine the number of ways to choose 7 locations out of the remaining 8 locations. This can be found using the combination formula.
The combination formula, also known as "n choose k," is given by the expression C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from and k is the number of items to choose.
In this case, there are 8 locations remaining and the driver needs to choose 7 of them. Applying the combination formula, we have C(8, 7) = 8! / (7! * (8-7)!) = 8! / (7! * 1!) = 8.
Therefore, there are 8 possible different routes for the delivery driver to make deliveries at the remaining 8 locations, given that the driver has time to make deliveries at 7 of them.
To simplify the answer, we can state that there are 8 possible different routes for the driver.
In summary, the number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.
For more such questions on delivery driver, click on:
https://brainly.com/question/25801071
#SPJ8
A shirt company has 3 designs each of which can be made with short or long sleeves. There are 6 color patterns available. How many different shirts are available from this company?
Answer:
36 different shirts-----------------
Given that there are 3 designs, 2 sleeve lengths, and 6 color patterns, we can multiply these values together:
3 designs × 2 sleeve lengths × 6 color patterns = 36So, there are 36 different shirts available from this company.
There are 36 different types of shirt available for this company.
Given that;
Number of design Company has = 3
Number of color pattern available = 6
Types of shirt (short or long sleeves) = 2
Now, We need to find the number of different types of shirts are available from this company.
Since, the number of different types of shirts can be calculated by multiplying Number of design Company has with Number of color pattern available also multiplying with Types of shirt (short or long sleeves).
Hence, By framing in equation form we get;
the number of different types of shirts is,
⇒ 3 × 6 × 2
⇒ 36
Therefore, We get;
There are 36 different types of shirt available for this company.
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ1
(x+3)(x+7)=0
Problem answered, solution and why!
[tex](x+3)(x+7)=0\\x=-3 \vee x=-7\\\\x\in\{-7,-3\}[/tex]
What is the area of the shaded region?
Answer:
80 mm²
Step-by-step explanation:
Even for slanted triangles, the area is base x half height! The base is 10 mm, half the height is 8 mm, so the area is 8x10=80 mm.
First to find correct answer will get brainly
The surface area of the dilated solid is 2,880 square units
What is the surface area of the dilated solid?Multiply each side of the shape by 4
Surface area of a rectangular prism = 2(LH + LW + WH)
Where,
Length, L = 8 × 4 = 32 units
Width, W = 6 × 4 = 24 units
Height, H = 3 × 4 = 12 units
Surface area of a rectangular prism = 2(LH + LW + WH)
= 2(32×12 + 32×24 + 24×12)
= 2(384 + 768 + 288)
= 2(1,440)
= 2,880 square units
Therefore, 2,880 square units is the surface area of the solid.
Read more on dilation:
https://brainly.com/question/3457976
#SPJ1
Zara's car depreciates at a rate of 14% per year.
By what percentage has Zara's car depreciated after 5 years?
Give your answer to the nearest whole number.
NO SPAM.
Answer:
53%
Step-by-step explanation:
You want to know the depreciation of car value after 5 years if it is 14% per year.
MultiplierThe multiplier of value each year is ...
1 + growth rate = 1 + (-14%) = 0.86
When the value has been multiplied by that 5 times, it has been multiplied by ...
0.86^5 ≈ 0.4704
This represents a change in value from the original value of ...
0.4704 -1 = -0.5296 = -52.96% ≈ -53%
Zara's car has depreciated by 53% after 5 years.
<95141404393>
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The exact value of the cosine of θ is given as follows:
a) 3/5.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:
Sine of angle = opposite side/hypotenuse.Cosine of angle = adjacent side/hypotenuse.Tangent of angle = opposite side/adjacent side = sine/cosine.Applying the Pythagorean Theorem, the hypotenuse length is given as follows:
x² = 6² + (-8)²
x² = 100
x = 10.
As the x-coordinate is used for the cosine, the cosine is given as follows:
cos(θ) = 6/10
cos(θ) = 3/5.
Learn more about trigonometric ratios at brainly.com/question/24349828
#SPJ1
The sum of two numbers is -6. One number is 14 more than the other one. Find the numbers.
Answer:
The two numbers are -10 and 4
Step-by-step explanation:
[tex]x+y=-6\\y=14+x\\\\x+(14+x)=-6\\2x+14=-6\\2x=-20\\x=-10\\\\x+y=-6\\-10+y=-6\\y=4[/tex]
Please help I don’t understand thank you have a blessed day
By evaluation, the values of the rational function are f(11) = - 1 / 12 and f(- 2) = 1, respectively.
How to evaluate a rational function
In this problem we find the case of a rational function that must be evaluated at two different x-values: x = 11, x = - 2. The procedure is summarized below:
Write the entire expression.Substitute on x with the given value.Simplify the expression by algebra properties.Now we proceed to present the complete procedure:
f(11) = 11 / (11 + 1) - 1
f(11) = 11 / 12 - 1
f(11) = 11 / 12 - 12 / 12
f(11) = (11 - 12) / 12
f(11) = - 1 / 12
f(- 2) = (- 2) / (- 2 + 1) - 1
f(- 2) = - 2 / (- 1) - 1
f(- 2) = 2 - 1
f(- 2) = 1
To learn more on evaluating functions: https://brainly.com/question/11270390
#SPJ1
1. Identify the variable that is contained in the expression.
7y+2y² +3
7
x
y
3
The variable that is contained in the given expression is y. Therefore, option C is the correct answer.
The given expression is 7y+2y² +3.
In the given expression there are 3 terms, so it is called trinomial.
In the term 7y, y is the coefficient of 7.
In the term 2y², y² is the coefficient of 2.
3 is the constant term.
Therefore, option C is the correct answer.
To learn more about an expression visit;
https://brainly.com/question/28170201.
#SPJ1
Stuck on this and cant move along until I get it correct. Please help.
Fill in the missing value.
The measure of angle F is ___°
The solution is: the measure of angles 2, 3, and 4 are:
m∠2 = 95°
m∠3 = 85°
m∠4 = 95°
Vertical Angle Theorem:
When two straight lines intersect, the opposite vertical angles formed are always equal (congruent) to each other.
Therefore,
m∠3 = 85°
m∠2 = m∠4
Linear pair:
Two adjacent angles which, when combined, form a line, so the sum of a linear pair is 180°.
Therefore,
85° + m∠2 = 180°
m∠3 + m∠4 = 180°
If 85° + m∠2 = 180°
⇒ m∠2 = 180° - 85°
⇒ m∠2 = 95°
As m∠2 = m∠4 then m∠4 = 95°
To learn more on angle click:
brainly.com/question/28451077
#SPJ1
complete question:
Find the measure of angles 2, 3, and 4. input the measures then click done. i-ready
please help i missed a day of class i cant figure this out
Can someone answer and provide an explanation for these problems? Find the midpoint of the line segment with the given endpoints.
52) The midpoint of the line segment is (-0.5, 9).
53) The midpoint of the line segment is (3, -8.5).
52) To find the midpoint of the line segment with endpoints (8,9) and (-9,9), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (x, y) are the average of the corresponding coordinates of the endpoints.
For the x-coordinate:
(x₁ + x₂) / 2 = (8 + (-9)) / 2 = (-1) / 2 = -0.5
For the y-coordinate:
(y₁ + y₂) / 2 = (9 + 9) / 2 = 18 / 2 = 9
Therefore, the midpoint of the line segment is (-0.5, 9).
53) To find the midpoint of the line segment with endpoints (8,-10) and (-2,-7), we apply the same process using the midpoint formula.
For the x-coordinate:
(x₁ + x₂) / 2 = (8 + (-2)) / 2 = 6 / 2 = 3
For the y-coordinate:
(y₁ + y₂) / 2 = (-10 + (-7)) / 2 = -17 / 2 = -8.5
Hence, the midpoint of the line segment is (3, -8.5).
for such more question on line segment
https://brainly.com/question/10496716
#SPJ11
Sofia and ella are both writing expressions to calculate the surface area of a rectangular prism however they wrote different expressions.
a. examine the expressions below, and determine if they represent the same value. explain why or why not.
sofia's expression
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm)
ella's expression:
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm)
b. what fact about the surface area of a rectangular prism does ella's expression show more clearly than sofia's?
a ) The given expression from Sofia and Ella represents two different values.
b.) The fact about the surface area of prism that Ella's expression shows that is not in Sofia's expression is that the expression is according to the formula.
How to determine the surface area of a rectangular prism?To determine the surface area of a rectangle prism, the formula that should be used would be given below:
That is;
Surface area of rectangular prism;
= 2(wl+hl+hw)
when the formula is multiplied out the following is gotten;
= 2wl + 2hl + 2hw
From Ella's expression,
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm). This follows the order of the formula. And it's final answer = 94cm²
From Sofia's expression,
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm). This doesn't follow the order of the formula and therefore is not correct and not the same final value with Ella's expression.
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1