Answer:
67,43/10 = 6.743
When dividing any number by 10, you just move the decimal to the left. When multiplying, you move it to the right.
Step-by-step explanation:
Hope it helps! =D
Find the area of a triangle with base of 6m and height of 15m
Answer:
45 meters
Step-by-step explanation:
[tex]Area=\frac{1}{2}bh\\ A=\frac{1}{2}(6)(15)\\ A=3(15)\\A=45[/tex]
⊱________________________________________________________⊰
Answer:
A=45 m²
Step-by-step explanation:
The formula for the area of a triangle is, [tex]\bigstar\underline{\boxed{\sf{A=\frac{bh}{2}}}}[/tex].
where :
[tex]\triangleright\sf{A=Area,b=base,h=height}\triangleleft[/tex]
Substitute the values,
[tex]\large\begin{gathered}\sf{A=\frac{6*15}{2} \\ \sf{A=\frac{90}{2}\\\bigstar\underline{\boxed{\sf{A=45 \ m^2}}}} \end{gathered}[/tex]
Done !! Hope this made sense to you :)
[tex]\small\boldsymbol{Calligraphy}[/tex]
⊱______________________________________________________⊰
Nan is 20 year old. In 8 years,she will be twice as old as Clarisse.how old is clarisse now?
Answer:
6
Step-by-step explanation:
The equation for this problem would be c = (20 + 8) / 2 - 8. Add 20 and 8 to get 28, divide 28 by 2 to get 14, then subtract 8 to get 6.
I need answers please help me
Answer:
the ansqer is g(x) = 4^x-4 + 2
What is the value of z in the equation 4(2z + 3) = 12?
−13
12
0
12
Answer:
0
Step-by-step explanation:
8z +12 = 12
8z = 0
z =0
Answer:
The answer is 0
Step-by-step explanation:
4(2z+3)=12?=
We use the distributive property to distribute the 4 into the 2.
8z=3=12?=
8 + 3 is 12 so the z has no part to play in this.
z=0
You could also have divided from both sides of the equation, but doing it this way is easier for me.
A group of people were asked if they had run a red light in the last year. 150 responded yes and 185 responded no. Find the probability that if a person is chosen at random, they have run a red light in the past year
The probability that a person chosen at random have run a red light in the past year is 0.45.
Given that 150 people have responded yes and 185 have responded no in a group of people when they asked whether they have run a red light.
Probability lies between 0 and 1. The value of probability can be find by :
Probability= Number items/total items.
Number of people who said that they have run red light=150
Number of people who said that they have not run red light=185
Total people=150+185
=335 people
Probability that a person chosen at random have run red light in the past year=
=Number of people who said that they have run red lights / total people
=150/335
=0.447
After rounding off it will be 0.45.
Hence the probability that a person chosen at random have run a red light in the past year is 0.45.
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a circular garden has a diiameter of 6 yards what is the area of the garden use 3.14 for Tt
Given the diameter of the circular garden, the area of the garden is 28.36 yd².
What is the area of the garden?The area of a circle is expressed as; A = πr²
Given that;
Diameter d = 6ydRadius r = d/2 = 6yd/2 = 3ydArea A = ?A = πr²
A = 3.14 × (3yd)²
A = 3.14 × 9yd²
A = 28.36 yd²
Given the diameter of the circular garden, the area of the garden is 28.36 yd².
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A building contractor is to dig a foundation 30 feet long, 12 feet wide, and 6 feet deep. The contractor pays $20 per load for trucks to remove the dirt. Each truck holds 8 cubic yards. What is the cost to the contractor to have all the dirt hauled away?
Answer:
$1800
Step-by-step explanation:
Volume of the foundation: 30*12*6 = 2160 cubic feet
we need to convert this into yards because a truckload is 8 cubic yards, 2160/3 = 720 cubic yd
One truckload is 8 cubic yards
# of truckloads needed: 720/8 = 90 truckloads
Cost: $20*90 = $1800
PLEASE NEED HELP
The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years. What proportion of crocodiles live between 17.5 and 20.5 years?
Find the z-table here.
0.3147
0.4068
0.5932
0.6853
Using the normal distribution, it is found that 0.4068 of crocodiles live between 17.5 and 20.5 years.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
[tex]\mu = 18, \sigma = 2.6[/tex]
The proportion of crocodiles live between 17.5 and 20.5 years is the p-value of Z when X = 20.5 subtracted by the p-value of Z when X = 17.5, hence:
X = 20.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20.5 - 18}{2.6}[/tex]
Z = 0.96
Z = 0.96 has a p-value of 0.8315.
X = 17.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 18}{2.6}[/tex]
Z = -0.19
Z = -0.19 has a p-value of 0.4247.
0.8315 - 0.4247 = 0.4068
0.4068 of crocodiles live between 17.5 and 20.5 years.
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9 cos(sin¯¹(x)) = √81 – 81x²
The equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S
To answer the question, we need to know what an equation is
What is an equation?An equation is a mathematical expression that show the relationship between two variables.
Given 9cos(sin¯¹(x)) = √(81 – 81x²), we need to show L.H.S = R.H.S
So, L.H.S = 9cos(sin¯¹(x))
= 9[√{1 - sin²(sin¯¹(x)}] (Since sin²y + cos²y = 1 ⇒ cosy = √[1 - sin²y])
9[√{1 - sin²(sin¯¹(x)}] = √9² × √{1 - sin²(sin¯¹(x)}]
= √[9² × {1 - sin²(sin¯¹(x)}]
= √[81 × {1 - sin²(sin¯¹(x)}]
= √[81 × {1 - x²}] (since sin²(sin¯¹(x) = [sin(sin¯¹(x)]² = x²)
= √(81 – 81x²)
= R.H.S
So, the equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S
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at a party 5/9 of the persons were men and the rest were women.if there was total 1260 persons find the number of women in the present
SOLUTION :
let total people in the party be x i.e. 1260
then , number of men = 5/9 of x
= 5/9 of 1260 = 5 × 140 = 700 men
now ,
number of women = Total person - (number of total men)
= ( 1260 - 700 ) women
= 560 women
________________________________
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simplify 5x(3x^2+2x-3)
Answer:
[tex]15x^3 +10x^2 - 15x[/tex]
Step-by-step explanation:
Hello!
Use the distributive property and multiply like terms.
Simplify[tex]5x(3x^2 + 3x - 3)[/tex][tex]5x(3x^2) + 5x(2x) + 5x(-3)[/tex][tex]15x^3 +10x^2 - 15x[/tex]The simplified form is [tex]15x^3 +10x^2 - 15x[/tex].
Please Help! Multiple Choice!
Using the z-distribution, the p-value would be given as follows:
b) 0.0086.
What are the hypothesis tested?At the null hypothesis we test if the means are equal, hence:
[tex]H_0: \mu_D - \mu_C = 0[/tex]
At the alternative hypothesis, it is tested if they are different, hence:
[tex]H_1: \mu_D - \mu_C \neq 0[/tex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given as follows:
[tex]\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086[/tex][tex]\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556[/tex]Hence, for the distribution of differences, they are given by:
[tex]\overline{x} = 12 - 14 = -2[/tex].[tex]s = \sqrt{0.6086^2 + 0.4556^2} = 0.76[/tex]What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
[tex]z = \frac{-2 - 0}{0.76}[/tex]
z = -2.63.
Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.
Hence option B is correct.
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where a=8a=8a, equals, 8 is a solution.
Answer:
a=0
Step-by-step explanation:
If this is what you are asking, and if I understand it correctly, 8*8=64 and not 8, but 8*0=0, therefore 0 is a solution.
Consider the function f denoted by:
[tex]f(x) = ln(x) [/tex]
Find the nth derivative of f(x) denoted by:
[tex]f {}^{(n)} (x ) [/tex]
Irrelevant answers will be reported immediately.
Step-by-step explanation:
Let take the first derivative
[tex] \frac{d}{dx} ln(x)) = x {}^{ - 1} [/tex]
The second derivative
[tex] - {x}^{ - 2} [/tex]
The third derivative
[tex]2 {x}^{ - 3} [/tex]
The fourth derivative
[tex] - 6 {x}^{ - 4} [/tex]
The fifth derivative
[tex]24 {x}^{ - 5} [/tex]
Let create a pattern,
The values always have x in it so
our nth derivative will have x in it.
The nth derivative matches the negative nth power so the nth derivative so far is
[tex] {x}^{ - n} [/tex]
Next, lok at the constants. They follow a pattern of 1,2,6,24,120). This is a factorial pattern because
1!=1
2!=2
3!=6
4!=24
5!=120 and so on. Notice how the nth derivative has the constant of the factorial of the precessor
so our constant are
[tex](n - 1)[/tex]
So far, our nth derivative is
[tex](n - 1)!x {}^{ - n} [/tex]
Finally, notice for the odd derivatives we are Positve and for the even ones, we are negative, this means we are raised -1^(n-1)
[tex] - 1 {}^{n -1} (n - 1) ! {x}^{-n} [/tex]
That is our nth derivative
how much must be deposited today to have $45,000 in 5 years with a quarterly compounding and an APR of 7.3%
Answer:
$31,341.81
Step-by-step explanation:
The compound amount equation is A = P(1 + r/n)^(nt), where P is the unknown principal, r is the annual interest rate, n is the number of compounding periods per year and t is the number of years. We want to solve this for P:
A
------------------- = P
(1 + r/n)^(nt)
Substituting the given numerical values;
$45,000
--------------------------- = P
(1+0.073/4)^(4*5)
Using a calculator, we evaluate this expression, obtaining: $31,341.81
a) Out of all items sent for refurbishing, %40 had mechanical defects, %50 had electrical
defects, and %25 had both. Denoting defectmechanicalahasitemanA and
defectmechanicalahasitemanB . Fill the probabilities into the Venn diagram and
determine the quantities listed below.
(i) AP [2 Marks]
(ii) BAP [1 Mark]
(iii) BAP c
i. P(A) = 0. 4
ii. P(AB) = 0. 9
iii. P(A∩B) =0. 25
How to determine the probability
From the information given,
Universal set = 40% + 50% + 25% = 0.40 + 0. 50 + 0. 25
A = Mechanical defects = 40%
B = Electrical defects = 50%
A∩B =25%
i. Probability of A , P(A)
= [tex]\frac{40}{100}[/tex]
= [tex]0. 4[/tex]
ii. Probability of B, P(AB)
= [tex]\frac{40}{100} + \frac{50}{100}[/tex]
= [tex]0. 4 + 0. 5[/tex]
= [tex]0. 9[/tex]
iii. Probability of A∩B entails the common factor between A and B
P(A∩B) = [tex]\frac{25}{100}[/tex] = [tex]0. 25[/tex]
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Q.3 Write the factors of 28 in circle A and the factors of 32 in circle B. Write
heir common factors in the common part of both. Which is the biggest
common factor of 28 &32?
Answer: The largest common factor of 28 and 32 is 4.
Step-by-step explanation:
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 32 are 1, 2, 4, 8, 16, 32
4)48 Ans: The average height of a group of boys was 145 cm. When 2 boys joined the group, the average height became 148 cm. Given that the average height of the 2 additional boys was 160 cm, find the number of boys in the group at first.
Answer:
8
Step-by-step explanation:
The definition of an average can be used with the given values to write an equation for the number of boys.
SetupThe average is the total divided by the number. If there were n original boys, the total was T, where ...
T/n = 145 ⇒ T = 145n
Adding two boys with an average of 160 cm height, the new total became (T +2(160)) and the new average became ...
(T +2(160))/(n +2) = 148 ⇒ T = 148(n +2) -320
Equating the values of T, we have ...
T = 145n = 148(n +2) -320
SolutionSolving for n, we find ...
0 = 3n -24 . . . . . . . . . . . . subtract 145n and simplify
0 = n -8 . . . . . . . . . . . divide by 3
8 = n . . . . . . . . . . . add 8
The number of boys in the group at first was 8.
Which of the following inequalities matches the graph?
Ox=-7
Oxs-7
Oys-7
Oyz-7
Answer:
Second option
Step-by-step explanation:
As its a solid line, it indicates the inequality contains equal to in it. As the line crosses the x - axis it must be an option whereby x > or x < . Now read the value which is 7 therefore x ≤ 7
The speed of the boat in still water is mph.
The speed of a river current is 3 mph. If a boat travels 30 miles downstream in the same time that it takes to travel 20 miles upstream, find the speed of the boat in still water.
Answer: the speed of the stream is 9mph
The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.
x –3 –2 0 1 2
h(x) 0 –23 –12 0 0
If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
h(x) = x3 + 6x2 + 11x – 6
h(x) = x3 – 7x + 6
h(x) = x3 – 7x – 6
h(x) = x4 + 2x3 – 7x2 – 8x + 12
The equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6
How to find the equation of a Polynomial?
From the given table, we see that the x-intercepts are;
(-3, 0), (1, 0) and (2, 0)
Now, we are told the the x-intercepts have a multiplicity of one which means they occur as roots only once. Thus, we can say that the roots in factor form are;
(x + 3), (x - 1), (x - 2)
Then, the polynomial will be;
h(x) = (x + 3) * (x - 1) * (x - 2)
h(x) = (x + 3)(x² - 3x + 2)
h(x) = x³ + 3x² - 3x² - 9x + 2x + 6
h(x) = x³ - 7x + 6
Thus, the equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6
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Find the equation of the line passing through the points (3,7) and (-2,5)
Answer:
The equation of the line passing through the points (3,7) and (-2,5) is y=⅖x+29/5
Step-by-step explanation:
Greetings !
[tex]first \: find \: the \: slope \: m \\ m = \frac{(Y₂-Y₁)}{(X₂-X₁)} ..substitute \: vlues \\ m = \frac{(5 - 7)}{( - 2 - 3)} = \frac{ - 2}{ - 5} = \frac{2}{5} \\ y = mx + b \: to \: find \: equation \: of \: aline \\ between \: two \: poins and \: use \: \\ one \: of \: the \: two \: points \: lets \: take( - 2.5) \\ y = mx + b \\ 5 = \frac{ - 2}{5} ( - 2) + b \\ 5 = \frac{ - 4}{5} + b \\ 5 + { - 4}^{5} = b \\ \frac{25 + 4}{5} = b \\ b = \frac{29}{5} \\ finally \: equation \: of \: the \: line \: will \: be \\ y = \frac{2}{5} x + \frac{29}{5} [/tex]
Find the measure of the ndicaited angle to the nearest degree 35 and 38
The measure of the indicated angle to the nearest degrees is 23 degrees.
How to find angle of a right angle triangle?The angle of a right angle triangle can be found as follows:
Therefore, the angle can be found using trigonometric ratios as follows;
cos ∅ = adjacent / hypotenuse
Therefore,
adjacent side = 35 units
hypotenuse side = 38 units
Hence,
cos ∅ = 35 / 38
∅ = cos⁻¹ 0.92105263157
∅ = 22.9272842944
∅ ≈ 23 degrees.
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Find the values of the variables in the parallelogram.
please help asap
tysm
Answer:
Step-by-step explanation:
What is the total repayment made, including principal and interest, on a loan of $1,100 at 3.5% interest compounded annually over four years?
The total repayment made, including principal and interest is $1262.27
Compound interestThe formula for calculating the compound interest is calculated as shown below;
A = P(1+r)^t
where
P is the principal = $1100
rate = 3.5% = 0.035
time "t" =4 years
Substitute
A. = 1100(1+0.035)^4
A = 1100(1.035)^4
A = 1100(1.14752)
A = 1262.27
Hence the total repayment made, including principal and interest is $1262.27
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Company A manufactures and sells gidgets. The owners have determined that the company has the monthly revenue and cost functions shown, such that x represents the number of gidgets sold.
R(x) = 16x
C(x) = 12x + 1,424
At what number of gidgets sold will the company break-even (the point where revenue equals cost)?
Considering the given equations for revenue and cost, the company will break-even when 356 widgets are sold.
What is the break-even point?The break-even point is the value of x for which:
R(x) = C(x).
In this problem, the functions are:
R(x) = 16x.C(x) = 12x + 1424.Hence:
R(x) = C(x)
16x = 12x + 1424
4x = 1424
x = 1424/4
x = 356
The company will break-even when 356 widgets are sold.
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what is the value of x 44 inches and 55 inches triangle
Answer: I don't know what you are talking about, but if x is the area, then the answer is 1,210.
Step-by-step explanation: 44 x 55 x 1/2 = 1,210. The formula for the area of a triangle is 1/2 times length times height. Therefore, x = 1,210
Hope this helps.
Find the Diameter of the Circle with the following equation. Round to the nearest tenth.
(x - 2)2 + (y + 6)2 = 35
The diameter of the circle is 11.8 units
How to determine the diameter of the circle?The circle equation is given as:
(x - 2)^2 + (y + 6)^2 = 35
A circle equation is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where
Diameter = 2r
By comparing both equations, we have
r^2 = 35
Take the square root of both sides
r = 5.9
Multiply by 2
2r = 11.8
Hence, the diameter of the circle is 11.8 units
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The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
The values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4
How to evaluate the function?As a general rule;
f⁻¹(f(x)) = x
This means that:
f⁻¹(f(6.022)) = 6.022
Also, we have:
f⁻¹(10) + f(-6)
From the table of values, we have:
f⁻¹(10) = -6 and f(-6) =10
So, we have:
f⁻¹(10) + f(-6) = -6 + 10
Evaluate
f⁻¹(10) + f(-6) = 4
Hence, the values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4
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a store marks up the wholesale price of a skateboard by 112%. The retail price is $35. What is the wholesale price of the skateboard?