Analyze the diagram below and answer the question that follows.

Answer:

24

Step-by-step explanation:

Formula

The area of a Trapezoid is given as

A = (b1 + b2)*h/2

Givens

b1 = 8

b2 = 4

h = 4

Solution

Area = (8 + 4)*4/2

Area = 12*4/2

Area = 24

Answer:

-4 please brainliest me

Step-by-step explanation:

9.68x+21.6-6.23x=2.3x+17

lets move it to the left

9.68x+21.6-6.23x-(2.3x+17)=0

Then, We add all the numbers together, and all the variables

3.45x-(2.3x+17)+21.6=0

We get rid of parentheses

3.45x-2.3x-17+21.6=0

We add all the numbers together, and all the variables

1.15x+4.6=0

We move all terms containing x to the left, all other terms to the right

1.15x=-4.6

x=-4.6/1.15

x=-4

x= -8 makes the equation true.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

9.68x + 21.6 -6.23x = 2.3x + 17​

Now, solving for x

9.68 x - 6.23x - 2.3x = 17 - 21.6

1.15x= -4.6

x= -4.6 / 1.15

x= -8

Hence, x= -8 makes the equation true.

Learn more about equation here:

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Answer:

5, yes.

Step-by-step explanation :

Answer:

B. F(x) = 3(x - 2)² - 2

Step-by-step explanation:

→The function F(x) narrowed, meaning the absolute value being multiplied to the function is greater than 1.

→The function F(x) flipped over the x-axis, this means that the number being multiplied has to be a negative.

→The function F(x) shifted to the left 2 units, this means there needs to be a 2 being added.

→The function F(x) shifted downwards 2 units, meaning there needs to be a 2 being subtracted from the whole function.

This gives us the correct answer of "B. F(x) = 3(x - 2)² - 2."

Answer:

a. Standard deviation: 4.082

Standard error: 2.041

b. The 95% confidence interval for the actual temperature is (298.5, 311.5).

Upper bound: 311.5

Lower bound: 298.5

c. Test statistic t=2.45

P-value = 0.092

d. There is no enough evidence to claim that the dial of the oven is not properly calibrated. The actual temperature does not significantly differ from 300 °F.

e. If we use a significance level of 10% (a less rigorous test, in which the null hypothesis is rejected with with less requirements), the conclusion changes and now there is enough evidence to claim that the dial is not properly calibrated.

This happens because now the P-value (0.092) is smaller than the significance level (0.10), given statististical evidence for the claim.

Step-by-step explanation:

The mean and standard deviation of the sample are:

[tex]M=\dfrac{1}{4}\sum_{i=1}^{4}(305+310+300+305)\\\\\\ M=\dfrac{1220}{4}=305[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{3}\cdot [(305-(305))^2+(310-(305))^2+(300-(305))^2+(305-(305))^2]}\\\\\\ s=\sqrt{\dfrac{1}{3}\cdot [(0)+(25)+(25)+(0)]}\\\\\\ s=\sqrt{\dfrac{50}{3}}=\sqrt{16.667}\\\\\\s=4.082[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=305.

The sample size is N=4.

When σ is not known, s divided by the square root of N is used as an estimate of σM (standard error):

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{4.082}{\sqrt{4}}=\dfrac{4.082}{2}=2.041[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

The t-value for a 95% confidence interval and 3 degrees of freedom is t=3.18.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=3.18 \cdot 2.041=6.5[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 305-6.5=298.5\\\\UL=M+t \cdot s_M = 305+6.5=311.5[/tex]

The 95% confidence interval for the actual temperature is (298.5, 311.5).

This is a hypothesis test for the population mean.

The claim is that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=300\\\\H_a:\mu\neq 300[/tex]

The significance level is 0.05.

The sample has a size n=4.

The sample mean is M=305.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.028.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.082}{\sqrt{4}}=2.041[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{305-300}{2.041}=\dfrac{5}{2.041}=2.45[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

This test is a two-tailed test, with 3 degrees of freedom and t=2.45, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>2.45)=0.092[/tex]

As the P-value (0.092) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.

If the significance level is 10%, the P-value (0.092) is smaller than the significance level (0.1) and the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °C does not significantly differ from 300 °C.

Answer:

b. There's no statistically significant linear relationship between the number of miles driven and the maintenance cost

Step-by-step explanation:

The p-value for the slope estimate show us how strong is the certainty that there are a linear relationship between both variables. In this case, the p-value for the slopes shows if there is a significant relationship between the number of miles driven and the maintenance cost.

If we have a high p-value like 0.7 we can said that there is no certainty in the linear relationship. it means that there's no statistically significant linear relationship between the number of miles driven and the maintenance cost.

Answer:

For someone who is a head coach - their expected income for the remainder of their professional coaching career will be

Expected income = 1×$41,389 + 2×$62,993 + 10×$104,485

Expected income = $1,212,225

Step-by-step explanation:

Professional basketball coaches may coach at one of three levels:

On average, the annual salary is given by

Using our P matrix, we have solved to find the fundamental matrix (we have called it the (I-Q) inverse matrix):

                      Assistant      Associate     Head

Assistant              6                     4              2

Associate             2                     6              6        

Head                    1                      2              10

For someone who is a head coach - what is their expected income for the remainder of their professional coaching career?

As per the given P matrix, for someone who is a head coach will be:

Assistant = 1 time

Associate = 2 times

Head = 10 times

Therefore, the expected income will be,

Expected income = 1×$41,389 + 2×$62,993 + 10×$104,485

Expected income = $1,212,225

Answer:

x = 6                        x = -1

Step-by-step explanation:

When we have absolute value equations, we get two solutions, one positive and one negative

2x - 5 =7             2x -5= -7

Add 5 to each side

2x-5+5 = 7+5         2x -5+5 = -7+5

2x =12                     2x = -2

Divide each side by 2

2x/2 =12/2               2x/2 = -2/2

x = 6                        x = -1

Answer:

6

Step-by-step explanation:

Similar triangles. MNE is ABC but 3/4 the size. Multiply each side by 3/4 to get lengths.

x = 8 *3/4 = 6

Answer:

x = 3.6 cm

Step-by-step explanation:

By the theorem of intersecting secants,

"If two secants are drawn from a point outside the circle, product of the lengths of the secant segment and its external segment are equal."

3(3 + y) = 2(2 + 6 + 3)

9 + 3y = 2 × 11

3y = 22 - 9

3y = 13

y = [tex]\frac{13}{3}[/tex] cm = 4.33 cm

Now we will apply theorem of intersecting chords to determine the value of x.

" When two chords intersect each other in a circle, product of their segments are equal"

[tex]x\times 5=6\times 3[/tex]

[tex]x=\frac{18}{5}[/tex]

[tex]x=3.6[/tex] cm

Therefore, x = 3.6 cm and y = 4.33 cm

Answer:

Janas rate is of 4 miles per day.

Step-by-step explanation:

Her rate is the number of miles she ran per day.

We can solve this using a rule of three.

In 7 days, she ran 28 miles. How many miles she ran a day, that is, in one day?

1 day - x miles

7 days - 28 miles

[tex]7x = 28[/tex]

[tex]x = \frac{28}{7}[/tex]

[tex]x = 4[/tex]

Janas rate is of 4 miles per day.

Answer:

10 successful throws

Step-by-step explanation:

40 free throws

25% (25)

40 x 0.25 = 10

Answer:

1/4

Step-by-step explanation:

1/2 times 1/2

1/2 because there is 3 odds and 3 evens

the total is 6

3/6 equals to 1/2

so 1/2 times 1/2 is 1/4

Answer:

y = 3x +1 (1)

2y = 6x +2  (2)

We can devide equation (2) by 2 and we got:

[tex] y =3x +1[/tex]   (3)

And since equations (1) and (3) are equal we can do this:

[tex] 3x +1 = 3x+1[/tex]

And that implies:

[tex] 0=0[/tex]

And for this case we will have infinite solutions for the sytem given since we have two lines equal

Step-by-step explanation:

For this case we have the following system of equations given:

y = 3x +1 (1)

2y = 6x +2  (2)

We can devide equation (2) by 2 and we got:

[tex] y =3x +1[/tex]   (3)

And since equations (1) and (3) are equal we can do this:

[tex] 3x +1 = 3x+1[/tex]

And that implies:

[tex] 0=0[/tex]

And for this case we will have infinite solutions for the sytem given since we have two lines equal

Answer:

6^5

Step-by-step explanation:

6 multiplied with itself 5 times is equal to 6^5

Answer:

1, 5, 25, 125, ...

3, 6, 12, 24, ...

Step-by-step explanation:

1, 5, 25, 125, ...

3, 6, 9, 12,...

3, 6, 12, 24, ...

3, 9, 81, 6, 561, ...

10, 20, 40, 60, ...

Answer:

Step-by-step explanation:

Consider the augments matrix (the right most column is  the extra vector).

[tex]\left[\begin{matrix} 1 & 4 & -2 \\3 & h & -6\end{matrix}\right][/tex]

By multypling the first row by 3 and substracting it from the second row and saving the result in the second row we get the matrix

[tex]\left[\begin{matrix} 1 & 4 & -2 \\0 & h-12 & 0\end{matrix}\right][/tex]

Note that since the value of the third column in the second row is 0, any value of h gives us a consistent system. An inconsistent system is when we get a row of zeros that is equal to a number different from 0.

Answer:

a) 10.08 gallons and $32.66 of gas

b) gallons used = n/25

c)cost of the gasoline = [tex]\frac{n}{25}(3.24)[/tex]

Step-by-step explanation:

a) We know that Kimberly has traveled 252 miles and we also know that her car gets 25 miles per gallon. We can apply proportions and rule of three:

25 miles ------ 1 gallon

252 miles ----- x gallons

Solving for x:

x gallons = 252 miles(1 gallon)/25 miles= 10.08 gallons.

Thus, she has used 10.08 gallons since she started driving.

Now we need to know the cost of the gasoline that she has used.

We know that each gallon of gas costs $3.24 and she has used 10.08 gallons. Again, we can apply proportions and rule of three:

1 gallon ------ 3.24 dollars

10.08 gallons---- x dollars.

Solving for x we get:

[tex]x=(10.08)(3.24)[/tex]= 32.659=32.66 dollars.

Thus, she has used $32.66 of gas since she started driving.

b) Write an expression in terms of n that represents the number of gallons of gasoline she has used since she started driving.

If we know that n is the number of miles that she drives, from what we wrote above, an expression to know the number of gallons she has used would be:

Gallons used = n/25 (since her car gets 25 miles per gallon) where n is the number of miles.

c) Write an expression in terms of n that represents the cost of the gasoline that she has used since she started driving.

Again, to know the cost of the gasoline we first need to know how many gallons she has used. From b) we know that the expression to know how many gallons she has used is n/25. Since each gallon costs $3.24 we will multiply this number by n/25 and we will get the cost (like we did in a))

Therefore, the cost of the gasoline = [tex]\frac{n}{25}(3.24)[/tex] where n is the number of miles.

Hey there! :)

Answer:

B.

Step-by-step explanation:

To find the solution to the inequality, we can begin by solving for 'x':

2x + 1 ≥ 3

Subtract 1 from both sides:

2x ≥ 2

Divide both sides by 2:

x ≥ 1.

This means that the graph must contain all values of x greater or equal to one. The only number line that shows solutions greater than 1 is B.

Answer:

The apple cost RS 18.24 per kg, while

the orange cost RS 91.18 per kg.

Step-by-step explanation:

Let the cost of 1kg if apple and orange be RS A and RS O respectively.

From the first line:

4A +6O= 620

2A +3O= 310 -----(1) (÷2 throughout)

From the information given in second line:

O= 5A -----(2)

subst. (2) into (1):

2A +3(5A)= 310

2A +15A= 310 (expand)

17A= 310 (simplify)

A= 310 ÷17 (÷17 on both sides)

A= 18.235 (5 s.f.)

A= 18.24 (2 d.p.)

Subst. into (2):

O= 5(18.235)

O= 91.18 (2 d.p.)

Answer:

27/(4x^6y^8)

Step-by-step explanation:

Target the variables first. (x^a)^b is the same as x^(a x b).

In the numerator, it is x^(2 x 3) , which is x^6, and y^(4 x 3), which is y^12.

Same principle on the bottom. the denominator is x^12 and y^20.

In the numerator, the number 4 is alone so don't do anything to it. Cube 3. The coefficient of the numerator is 4 x 3^3 . The coefficient of the denominator is 2^4. Cancel like terms. when you divide same terms' exponents, you subtract the exponent on top by the exponent on the bottom. Remember that you can only simplify LIKE terms. (x with x, y with y, number with number.)

Answer:

[tex]\frac{64}{125}[/tex]

Step-by-step explanation:

[tex]\frac{12}{15} \div \frac{25}{16}[/tex]

[tex]\frac{12}{15} \times \frac{16}{25}[/tex]

[tex]\frac{12 \times 16}{15 \times 25}[/tex]

[tex]\frac{192}{375}[/tex]

[tex]\frac{64}{125}=0.512[/tex]

Answer:

[tex]\frac{64}{125}[/tex]

Step-by-step explanation:

=> [tex]\frac{12}{15} / \frac{25}{16}[/tex]

Changing the division sign into multiplication and inverting the term after the sign.

=> [tex]\frac{12}{15} * \frac{16}{25}[/tex]

=> [tex]\frac{12*16}{15*25}[/tex]

=> [tex]\frac{192}{375}[/tex]

=> [tex]\frac{64}{125}[/tex]

This is the required form.

Answer:

[tex]\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]

Step-by-step explanation:

Volume of water in the tank = 1000 L

Let y(t) denote the amount of salt in the tank at any time t.

Initially, the tank contains 60 kg of salt, therefore:

y(0)=60 kg

Rate In

A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.

[tex]R_{in}[/tex] =(concentration of salt in inflow)(input rate of solution)

[tex]=(0.03\frac{kg}{liter})( 9\frac{liter}{min})=0.27\frac{kg}{min}[/tex]

Rate Out

The solution is mixed and drains from the tank at the same rate.

Concentration, [tex]C(t)=\dfrac{Amount}{Volume} =\dfrac{y(t)}{1000}[/tex]

[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)

[tex]=\dfrac{y(t)}{1000}* 9\dfrac{liter}{min}=0.009y(t)\dfrac{kg}{min}[/tex]

Therefore, the differential equation for the amount of Salt in the Tank  at any time t:

[tex]\dfrac{dy}{dt}=R_{in}-R_{out}\\\\\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]

Answer:

Step-by-step explanation:

Answer: 1. (4, 8); 2. (3, 4)

Step-by-step explanation: I tried to get this to you fast but I can give you an explaination if you would like one :)

Answer:

360 miles

Step-by-step explanation:

Step-by-step explanation:

work is shown and pictured

9514 1404 393

Answer:

  32°

Step-by-step explanation:

The law of cosines can be used for this:

  h^2 = f^2 +g^2 -2fg·cos(H)

  cos(H) = (f^2 +g^2 -h^2)/(2fg)

  cos(H) = (650,500/763,600)

  H = arccos(6505/7636) ≈ 31.5826°

Angle H is about 32°.