Answer:
A) The height of the trapezoid is 6.5 centimeters.
B) We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex]. [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex]
C) The length of the other base of the trapezoid is 20 centimeters.
D) We can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. [tex]b = \frac{A}{h}[/tex]
Step-by-step explanation:
A) The formula for the area of a trapezoid is:
[tex]A = \frac{1}{2}\cdot h \cdot (b_{1}+b_{2})[/tex] (Eq. 1)
Where:
[tex]h[/tex] - Height of the trapezoid, measured in centimeters.
[tex]b_{1}[/tex], [tex]b_{2}[/tex] - Lengths fo the bases, measured in centimeters.
[tex]A[/tex] - Area of the trapezoid, measured in square centimeters.
We proceed to clear the height of the trapezoid:
1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.
2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.
3) [tex]2\cdot A\cdot (b_{1}+b_{2})^{-1} = (2\cdot 2^{-1})\cdot h\cdot [(b_{1}+b_{2})\cdot (b_{1}+b_{2})^{-1}][/tex] Compatibility with multiplication/Commutative and associative properties.
4) [tex]h = \frac{2\cdot A}{b_{1}+b_{2}}[/tex] Existence of multiplicative inverse/Modulative property/Definition of division/Result
If we know that [tex]A = 91\,cm^{2}[/tex], [tex]b_{1} = 16\,cm[/tex] and [tex]b_{2} = 12\,cm[/tex], then height of the trapezoid is:
[tex]h = \frac{2\cdot (91\,cm^{2})}{16\,cm+12\,cm}[/tex]
[tex]h = 6.5\,cm[/tex]
The height of the trapezoid is 6.5 centimeters.
B) We should follow this procedure to solve the formula for [tex]b_{1}[/tex]:
1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.
2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.
3) [tex]2\cdot A \cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot (b_{1}+b_{2})[/tex] Compatibility with multiplication/Commutative and associative properties.
4) [tex]2\cdot A \cdot h^{-1} = b_{1}+b_{2}[/tex] Existence of multiplicative inverse/Modulative property
5) [tex]\frac{2\cdot A}{h} +(-b_{2}) = [b_{2}+(-b_{2})] +b_{1}[/tex] Definition of division/Compatibility with addition/Commutative and associative properties
6) [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex] Existence of additive inverse/Definition of subtraction/Modulative property/Result.
We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex].
C) We can use the result found in B) to determine the length of the remaining base of the trapezoid: ([tex]A= 215\,cm^{2}[/tex], [tex]h = 8.6\,cm[/tex] and [tex]b_{2} = 30\,cm[/tex])
[tex]b_{1} = \frac{2\cdot (215\,cm^{2})}{8.6\,cm} - 30\,cm[/tex]
[tex]b_{1} = 20\,cm[/tex]
The length of the other base of the trapezoid is 20 centimeters.
D) Yes, we can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. Now we present the procedure to clear [tex]b[/tex] below:
1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.
2) [tex]b_{1} = b_{2}[/tex] Given.
3) [tex]A = \frac{1}{2}\cdot h \cdot (2\cdot b)[/tex] 2) in 1)
4) [tex]A = 2^{-1}\cdot h\cdot (2\cdot b)[/tex] Definition of division.
5) [tex]A\cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot b[/tex] Commutative and associative properties/Compatibility with multiplication.
6) [tex]b = A \cdot h^{-1}[/tex] Existence of multiplicative inverse/Modulative property.
7) [tex]b = \frac{A}{h}[/tex] Definition of division/Result.
Suppose that Elsa and Frank determine confidence intervals based on the same sample proportion and sample size. Elsa uses a larger confidence level than Frank. How will midpoint and width of confidence intervals compare
Answer:
elsa's interval width will be greater than that of frank
Step-by-step explanation:
first of all we are told that both Elsa and Frank have the same sample proportion so their midpoint is also going to be the same.
now as the confidence level goes higher, so also would the margin of error increase. then the width of the confidence interval would rise so it can be more confident.
from this question elsa has a larger confidence level therefore her intervals width will be greater than franks own.
Write the equation of the line:
(0,3); slope -2
Answer:
y=-2x+3
Step-by-step explanation:
the y-intercept is (0,3) and the slope is -2, just plug that in to the slope intercept form, y=mx+b
Pls mark as brainliest thank u.
Try it
Solve the system of equations.
2x + 3y = 1
5x + 2 = 8
What is the solution?
Answer:
x=6/5 ,y= -7/15
Step-by-step explanation:
we are going to solve this simultaneously.
2x+3y=1.......(i)
and
5x+2=8
5x=6
x= 6/5 .......(ii)
Now let's put value of x into equation number (i)
2x+3y=1
2(6/5) +3y=1
12/5 +3y =1
3y= 1-(12/5)
3y = -7/5
y = (-7/5) ÷3
y= -7/15
According to the Fiji Diabetes Association, 23.1% of Fijians aged 60 years or older had diabetes in 2017. A recent random sample of 200 Fijians aged 60 years or older showed that 52 of them have diabetes. Using a 5% significance level, perform a test of hypothesis to determine if the current percentage of Fijians aged 60 years or older who have diabetes is higher than that in 2017. Use the P-value method
Answer:
The point estimated is 0.260
Step-by-step explanation:
The computation is shown below:
Sample in which the people have diabetes = 52
Random sample = 200
Significance level = 5%
Based on this, the, estimation point is
= Sample in which the people have diabetes ÷ Random sample
= 52 ÷ 200
= 0.260
hence, the point estimated is 0.260
We simply applied the above formula
And, the same is to be considered
The Null Hypothesis is accepted because the value of z is 0.973 and this can be determined by performing the test of the Hypothesis.
Given :
Association, 23.1% of Fijians aged 60 years or older had diabetes in 2017.A recent random sample of 200 Fijians aged 60 years or older showed that 52 of them have diabetes.Use a 5% significance level.Hypothesis are as follows:
Null hypothesis, [tex]\rm H_0: p\leq 0.231[/tex]
Alternate hypothesis, [tex]\rm H_a : p>0.231[/tex]
Now, performing the test of the hypothesis. The critical value z is given by:
[tex]z = \dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0(1-p_0)}{n}}}[/tex] ----- (1)
Now, the value of [tex]\hat {p}[/tex] is given by:
[tex]\hat{p}=\dfrac{52}{200} = 0.26[/tex]
Now, put the values of known terms in equation (1).
[tex]z = \dfrac{0.26-0.231}{\sqrt{\dfrac{0.231\times 0.769}{200}}}[/tex]
[tex]z = \dfrac{0.029}{0.0298}[/tex]
z = 0.973
Therefore, the null hypothesis is accepted.
For more information, refer to the link given below:
https://brainly.com/question/19613147
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-10x^2+600x-3588
y=−10x
2
+600x−3588
Answer:
Step-by-step explanation:
The maximum profit will be found in the vertex of the parabola, which is what your equation is. You could do this by completing the square, but it is way easier to just solve for h and k using the following formulas:
[tex]h=\frac{-b}{2a}[/tex] for the x coordinate of the vertex, and
[tex]k=c-\frac{b^2}{4a}[/tex] for the y coordinate of the vertex.
x will be the selling price of each widget and y will be the profit. Usually, x is the number of the items sold, but I'm going off your info here for what the vertex means in the context of this problem.
Our variables for the quadratic are as follows:
a = -10
b = 600
c = -3588. Therefore,
[tex]h=\frac{-600}{2(-10)}=30[/tex] so the cost of each widget is $30. Now for the profit:
[tex]k=-3588-(\frac{(600)^2}{4(-10)})[/tex] This one is worth the simplification step by step:
[tex]k=-3588-(\frac{360000}{-40})[/tex] and
k = -3588 - (-9000) and
k = -3588 + 9000 so
k = 5412
That means that the profit made by selling the widgets at $30 apiece is $5412.
Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].
What is the maximum profit?
Maximum profit, or profit maximisation, is the process of finding the right price for your products or services to produce the best profit.
Here given that,
A company sells widgets. The amount of profit, [tex]y[/tex], made by the company, is related to the selling price of each widget, [tex]x[/tex], by the given equation.
As the maximum profit found in the vertex of the parabola,
Here, [tex]x[/tex] will be the selling price of each widget and [tex]y[/tex] will be the profit.
The number of items sold is [tex]x[/tex].
So, the quadratic equation is:-
[tex]a = -10b = 600c = -3588.[/tex]
Therefore, so the cost of each widget is $[tex]30[/tex].
For the profit:-
[tex]k = -3588 - (-9000) andk = -3588 + 9000 sok = 5412[/tex]
Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].
To know more about the maximum profit
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if you subtract 19 from my number and multiply the difference by -2, the result is -8
Answer:cool
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
let the number be 'a'
-2(a - 19)= -8
open the brackets
-2a + 38 = -8
collect like terms
38 + 8 = 2a
46 = 2a
a = 23
1. In 1995, the average level of mercury uptake in wading birds in the Everglades was 15 parts per million. If we assume that the distribution of mercury uptake has a standard deviation of 1 part per million, and a current sample of 25 wading birds has an average of 14.6 parts per million. Which null and alternative hypotheses would be used to test that the level of mercury uptake in the Everglades has decreased since 1995?
Answer:
We reject H₀, we find that the current level of mercury uptake in the Everglades has decrease
Step-by-step explanation:
We need to test the current wading bird average 14,6 vs the 1995 average. As sample mean is 14,6 and population mean is 15 we are going to check test is of one tail (left tail test)
Test Hypothesis:
Null hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ < μ₀
Sample size 25 then n < 30 we will use t-student table
Population mean : μ₀ = 15 ppm
sample mean : μ = 14,6 ppm
sample standard deviation: s = 1 ppm
Sample size n : 25
degrees of freedom df = n - 1 df = 24
We will develop the test for CI 90% then α = 10% α = 0,1 α/2 = 0,05
For that values in t student table we find:
t(c) = 1,711 by symmetry t(c) = - 1,711
To compute ts
t(s) = ( μ - μ₀ ) / s/√n
t(s) = 14,6 - 15 / 1 /√25
t(s) = - 0,4*5 / 1
t(s) = - 2
Comparing t(c)and t(s)
|t(s)| > |t(c) | and t(s) < t(c) -2 < -1,711
Therefore t(s) in in the rejection region, we reject H₀
what is the pattern 2 10 40 120
Answer:
2 plus 3
Step-by-step explanation:
A lumber supplier sells 96-inch pieces of oak. Each piece must be within ¼ of an inch of 96 inches. Write and solve an inequality to show acceptable lengths.
Answer:
[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]
Step-by-step explanation:
Given that a lumber supplier sells 96 inch Pieces of oak which must be within 1/4 of an inch.
This situation can be represented by the following absolute value inequality:
[tex]|x \: - 96| \: \leqslant \: \frac{1}{4} [/tex].
The absolute value can be thought of as the size of something because length cannot be negative. The length must be no more than 1/4 away from 96.
To simplify this, pretend this is a standard equality, |x-96| = 1/4. 1/4 is the range of acceptable length, 96 is the median of the range, and x is the size of the wood.
First apply the rule |x| = y → x = [tex]\pm[/tex]y
|x-96| = 1/4
x - 96 = [tex]\pm[/tex]1/4
x = [tex]96 \pm 1/4[/tex]
(These are just the minimum, and maximum sizes)
Now with a less than or equal to, the solutions are now everything included between these two values.
Therefore:
[tex]96 - 1/4 \: \leqslant x [/tex] [tex]\leqslant \: 96 + 1/4 [/tex]
With less than inequalities, you must have the lower value on the left, and the higher value on the right.
If x represents the size of the pieces, then the acceptable lengths are represented by this following inequality:
[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]
This is interpreted as x (being the size of the oak) is greater than or equal to 95 3/4, and less than or equal to 96 1/4 in inches.
he cost of manufacturing a particular videotape is C(x)90009x, where x is the number of tapes produced. The average cost per tape, denoted by , is found by dividing by x. Find .
Answer:
The average cost per tape is 10.
Step-by-step explanation:
The cost of manufacturing a particular videotape is :
C(x) = 9000+9x
Where
x is the number of tapes produced.
We need to find the value of average per tape i.e. [tex]\lim_{x \to 9000} \bar C(x)[/tex]
[tex]\bar C(x)=\dfrac{9000+9x}{x}\\\\=\dfrac{9000}{x}+9\\\\ \lim_{n \to 9000} \bar C(x)=\dfrac{9000}{9000}+9\\\\=1+9\\\\=10[/tex]
So, the average cost per tape is 10.
Tickets for a drumline competition cost $5 at the gate and $3 in advance. One hundred more tickets were sold in advance than at the gate. The total revenue from ticket sales was $1990. How many tickets were sold in advance?
Answer:
The number of tickets sold at the gate is [tex] G = 211.25[/tex]
The number of tickets sold in advance is [tex] A = 311.25 [/tex]
Step-by-step explanation:
From the question we are told that
The cost of a tickets at the gate is [tex]a = \$ 5[/tex]
The cost of a ticket in advance is [tex]b = \$ 3[/tex]
Let the number of ticket sold in the gate be G
Let the number of ticket sold in advance be A
From the question we are told that
One hundred more tickets were sold in advance than at the gate and this can be mathematically represented as
[tex]G + 100 = A[/tex]
From the question we are told that
The total revenue from ticket sales was $1990 and this can be mathematically represented as
[tex]5 G + 3A = 1990[/tex]
substituting for A in the equation above
[tex]5 G + 3[G + 100]= 1990[/tex]
[tex]5 G + 3G + 300= 1990[/tex]
[tex] 8G + 300= 1990[/tex]
[tex] 8G = 1690[/tex]
=> [tex] G = 211.25[/tex]
Substituting this for G in the above equation
[tex]5 [211.25] + 3A = 1990[/tex]
=> [tex] 3A = 1990 - 1056.25[/tex]
=> [tex] A = 311.25 [/tex]
PLEASE HELP
ILL GIVE BRAINLIEST
Answer:
f(7x−1)=63x−16
Step-by-step explanation:
Answer:
x=3
Step-by-step explanation:
since f(x) and g(x) are equal, we can make the equation, 9x-7 = 7x - 1
9x = 7x + 6, 2x = 6, x = 3
The table below shows the weekly change in the price of one gram of gold for four weeks.
ONE GRAM OF GOLD
Week
Weekly Change in the Price (dollars)
1
+ 1.
2
-3.
3
+ 2.
4
+3.
By how much did the price of one gram of gold change from the beginning of week 1 to the end of week 4? Did the price increase or decrease? explain
At the end of week 4, the price per gram of gold was $39. What was the price per gram of gold at the beginning of week 1?
Show your work in the box below.
Answer _____________ price per gram of gold
Answer:
THEY DIDN'T IT WAS BECAUSE THEY MADE UP A FAKE RUMER AND HAD TO MAKE IT LOOK REAL
Step-by-step explanation:
Please help!!
x^2-2x+1-9y^2
Answer:
[tex]\left(x-1+3y\right)\left(x-1-3y\right)[/tex]
Step-by-step explanation:
[tex]x^2-2x+1-9y^2\\\\factor(skip for time)\\\\\left(x-1\right)^2-9y^2\\\\[/tex]
A little algebra process later...
you got the answer
Hoped this helped ya
<3
RedAnswer:
(x-1-3y) x (x-1+3y)
Step-by-step explanation:
x^2-2x+1-9y^2
Using a^2 - 2ab + b^2 = (a-b)^2 (factor the expression) = (x-1)^2 - 9y^2
(x-1)^2 - 9y^2 = (x-1-3y) x (x-1+3y) should be the answer :)
3g+h=18 2g+3h=26 what is h and what is g
Answer:
g=4 h=6
Step-by-step explanation:
3g +h = 18 (Equation 1)
2g+3h=26 (Equation 2)
From equation 1
3g+ h =18
h= 18-3g (equation 3)
substitute equation 3 into equation 2
2g+3h= 26
2g+ 3(18-3g)= 26
2g+3×18+3(-3g)=26
2g+54-9g=26
9g-2g= 54-26
7g=28
7g÷7 = 28÷7
g= 4
substitute g into equation 1
3g+h=18
3(4)+ h= 18
12+h= 18
h=18-12
h= 6
Answer:
g = 4; h = g
Step-by-step explanation:
When solving an equation with two variables, the goal is to isolate at least one of the variables so that you can plug it in to the equation to get the other. There are multiple ways to solve this so I'll just be giving one.
3g + h = 18
2g + 3h = 26
In these two equations, I notice that if I multiply the first equation by 3, the two equations will have the same values of h, so I'd be able to isolate g:
9g + 3h = 54
2g + 3h = 26
Now, subtract the second equation from the first to isolate g:
9g + 3h = 54
-2g + 3h = 26
= 7g = 28
= g = 4
Now that we have solved for g, we can plug it into either of the equations and solve for h:
2(4) + 3h = 26
= 8 + 3h = 26
= 3h = 18
= h = 6
And in conclusion, g = 4 and h = 6.
PLEASE HELP Please i don’t understand
Answer:
answer is 5
Step-by-step explanation:
f(5)= -5×5^2+26×5
= -125+130
= 5
A dog-washing salon is filling up the tub to was a dog. When the employee got to the tub,
there were already 2 gallons of water in the tub. She will fill the tub at a rate of 3 gallons a
minute.
Answer:
If there was 2 gallons in the tub at the moment, it must mean that it has been 2/3 of a minute or 40 seconds.
The two rates would be 3:60 and 2:40 and so on 1:20
Step-by-step explanation:
Good luck! Hope this helps! <3
What is the absolute value of 5,234?
Answer:
Step-by-step explanation:
5.234
Need help got until 12:10
From a circular sheet of paper with a radius 20 cm, four circles
of radius 5 cm each are cut out. What is the ratio of the uncut to
the cut portion?
Answer:
3 : 1
Step-by-step explanation:
The biggest circle has a radius of 20 cm
So that means, its area will be,
Area = [tex]\pi r^{2}[/tex]
Area = [tex]\pi * 20^{2}[/tex]
A = [tex]\pi * 400[/tex]
=> A = 400[tex]\pi[/tex]
We do not need to solve this because it is nit required
Then, one small circle has an area of,
Area = [tex]\pi r^{2}[/tex]
Area = [tex]\pi *5^{2}[/tex]
Area = [tex]\pi *25[/tex]
=> Area = 25[tex]\pi[/tex]
As there are 4 circles in, we get that the area covered by the small squares,
=> [tex]25\pi * 4[/tex]
=> [tex]100\pi[/tex]
So, the amount shaded = 100/400 (We can omit the [tex]\pi[/tex] at this stage because we are finding out a ratio)
=> 1/4
So, there is 1 cut region and the remaining is the uncut region,
As we need to find uncut to cut, the ratio will be,
=> remaining : 1
=> 3 : 1
If my answer helped, kindly mark me as the brainliest!!
Thanks!!
If you roll a die once, what is the probability of rolling a 3?
Answer:
1/6
Step-by-step explanation:
there are 6 sides, and 3 is one of the 6 sides. thus, the answer is 1/6
Answer:
1/6
Step-by-step explanation: there are 6 incomes and 1 number 3 in a die
Graph the line y-3=-1/3(x+2)
Slope: 1/2
y-intercept(s): (0, 7/3)
x: 0, 7
y: 7/3, 0
Step-by-step explanation:
y=-3 -1/3(1+2)=2/3.3=1.3=3
y=3
How many years will it take for Steven to make a total of $21,200?
(7 points)
12
8
6
10
Pls answer fast Y=Mx+b for x
Answer:
y=mx+b
y=mx+b-b
y-b=mx
y-b/m = mx/m
y-b/m = x
Answer:
x = (y - b)/M.
Step-by-step explanation:
y = Mx + b
Mx = y - b
x = (y - b)/M.
HELP ASAP IT'S AN EMERGENCY
________ and ________ are two ways that substances pass through a cell membrane out of the cell. A Photosynthesis, diffusion B Diffusion, active transport C Active transport, mitosis D Photosynthesis, mitosis
Answer:
b. diffusion and active transport
Step-by-step explanation:
these are two ways that substances, like nutrients, pass through cell membranes.
Answer:
b
Step-by-step explanation:
What is 837 divided by 27
Answer: 31
Step-by-step explanation: long division
What is the slope of the line? Select the correct choice below and, if necessary, fill in the answer box to complete
your choice.
O A. The slope of the line is
(Type an integer or a simplified fraction.)
O B. The slope of the line is undefined.
[tex]\tt Step-by-step~explanation:[/tex]
Slope = rise/run
[tex]\tt Steps:[/tex]
Rise: The line travels 5 units vertically (up) from the first point to the second.
Run: The line goes 6 units horizontally (left) from the first point to the second.
Slope = rise/run; Slope = 5/6
[tex]\Large\boxed{\tt The~slope~of~the~line~is:~\frac{5}{6}~units }[/tex]
Answer:
Slope = rise/run
Step-by-step explanation:
A stick is broken into two pieces, at a uniformly random breakpoint. Find the CDF and average of the length of the longer piece.
Answer:
Step-by-step explanation:
See attachment
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.18 F and a standard deviation of 0.65 F. Using the empirical rule, find each approximate percentage below.
a.
What is the approximate percentage of healthy adults with body temperatures within 3 standard deviation of the mean, or between 96.23 F and100.3 F?
Answer:
99.7%
Step-by-step explanation:
Empirical rule formula states that:
• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
From the question, we have mean of 98.18 F and a standard deviation of 0.65 F
The approximate percentage of healthy adults with body temperatures between 96.23 F and100.13 F is
μ - 3σ
= 98.18 - 3(0.65)
= 98.18 - 1.95
= 96.23 F
μ + 3σ.
98.18 + 3(0.65)
= 98.18 + 1.95
= 100.13 F
Therefore, the approximate percentage of healthy adults with body temperatures between 96.23 F and 100.13 F which is within 3 standard deviations of the mean is 99.7%