Evaluate 11 − 2(12 + 4) ÷ 2^2 need step by step process, thanks.

Answer:

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The volume of C.a .cylinder is twice the volume of a cone.

The formula fro the cylinder is πr²h and that of the cone is ⅓ the volume It should be noted that the volume of a cone can be equated to theone-third of the volume of a cylinder , this can be established when they are having same base radius and height.

The cylinder's volume  can be expressed as π r² h,  along with the surface area  which can be expressed as 2π r h + 2π r² and this can be used to get the values.

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Answer:

Step-by-step explanation:

Given that:

A study is conducted and the study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands.

a)

Thus; we formulate the null and the alternative hypotheses as follows:

The proportion is ; \(\frac{64}{100}\) = 0.64

Null hypothesis:    \({H_0}:p = 0.64\)  

The Null hypothesis states that there is no evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

Alternative hypothesis: \({H_a}:p \ne 0.64H\)

The Alternative hypothesis states that there is evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

b)

The proportion of the population = 0.64

The sample size n = 100

The number of shoppers = 52  stating that the supermarket brand was as good as the national brand

The sample proportion \(\hat p = \frac{52}{100}\)

\(\hat p = 0.52\)

The z - value is calculated by the formula:

\(z = \dfrac{\hat p-p}{\frac{\sqrt{ p(1-p)}}{100 }}\)

\(z = \dfrac{0.52-0.64}{\frac{\sqrt{ 0.64(1-0.64)}}{100 }}\)

\(z = \dfrac{-0.12}{0.048 }}\)

z = -2.50

Since z = -2.50

the p-value = 2P(Z ≤ -2.50)

p-value = 2 × 0.0062

The p-value = 0.0124

c)

At  significance level,  ∝ = 0.05 ; The p-value = 0.0124

According to  the rejection rule, if p-value is less than 0.05 then we will reject null hypothesis at ∝ = 0.05

Hence, the p-value =0.0124 < ∝ (=0.05)

According to the reject rule; reject null hypothesis.

Conclusion: There is no evidence at all that the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%.

d) we know that the significance level of ∝  = 0.05

The value\({z__{0.05}}\)  is obtained as:

\(P\left( {\left| Z \right| \le z} \right) = 0.05\)

Now; to determine Z ; we locate the probability value of 0.05 form the table of standard normal distribution. Then we proceed to the left until the  first column is reached and  the value is 1.90. Also , we move upward until we reach the top and the value is 0.06. Now; the intersection of the row and column results the area  to the left of z

This implies that :\(P(Z \leq -1.96)=0.05\)

The critical value for left tail is -1.96 and the critical value for right tail is 1.96.

Conclusion:

The critical value is -1.96 and the value of test statistic is - 2.50.  Here, we can see that  the value of test statistic is lesser than the critical value. Hence, we can be concluded that there is evidence that reject the null hypothesis.

Therefore, Yes, the national brand ketchup manufacturer is pleased with the conclusion.

Following are the solution to the given points:

For point a:

Calculation of the hypotheses:

Null hypothesis \(\ H_0:p=0.64 \\\\\)

Alternative hypothesis \(\ H_a : p \neq 0.64\)

For point b:

 Checking the value:  

\(\to np_0=100 \cdot 0.64=64>5\\\\\to n(1-p_0)=100\cdot(1-0.64)=100 \cdot 0.36= 36 > 5\)

Test statistic:

\(\to Z= \frac{0.52-0.64}{\sqrt{\frac{0.64 \times 0.36}{100} }}=-2.50\)

Since there are two-sided for the test. so, \(z=-2.50\) is negative.

Calculation of the P-value:  \(\to p=2P(z \leq -2.50)=2 \cdot 0.00621=0.01242<\alpha =0.05\)

For point C:

In this choice, the Null hypothesis value should be rejected.

For point D:

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The most specific name for the quadrilateral is trapezoid, the correct option is C.

A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.

Given;

The figure with 4 sides and two opposite are equal

Now,

In the figure two opposite sides are equal in length

But they all are not parallel only on pair of opposite sides are parallel.

Also, the figure the adjacent angle are equal.

Therefore, the quadrilateral will be trapezoid.

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A) From the table, the greatest amount of rainfall is 3 1/4 in, and the least amount of rainfall is 3/4 in. The difference between these values is:

B) The most common amount of rainfall is 2 3/4 in. If in the last two months the amount of rainfall is 2 3/4 in, then it will fall:

Answer:

Step-by-step explanation:

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I answered it here.

Answer:

None

Step-by-step explanation:

2a + 20/4

2a + 5

Best of Luck!

Answer:

2.0976637e+27 x+y+z x = x 80538738812075974, y = 80435758145817515, and z = 12602123297335631.

Step-by-step explanation: its right do the math this took me hours

Answer:

d. (-2.8,-2.6)​

Step-by-step explanation:

The solution is whwere the lines intersect

d. (-2.8,-2.6)​

Answer:

a)

slope = (-4 cm) / (650 cm)

slope ≈ -0.00615

b)  the section of the road measured horizontally is approximately 3983.74 cm long.

Step-by-step explanation:

change in horizontal distance = (change in vertical distance) / slope

change in horizontal distance = (-24.5 cm) / (-0.00615)

change in horizontal distance ≈ 3983.74 cm

According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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Answer:

3 hours?

Step-by-step explanation:

The number of times the students on your floor order pizza in a week, population.

A population is a complete set of individuals or objects that share common characteristics. It is an entire group of people, animals, plants, or objects that can be studied. A population can also be a group of people living in a certain geographical area.

A sample is a subset of a population. It is a smaller group of individuals or objects drawn from the population that are used to make inferences about the population as a whole.

A sample is used in statistical analysis to estimate population characteristics, such as mean, median, and variance. The accuracy of the estimates depends on the size and representativeness of the sample.

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The complete question is:

Determine whether the statement describes a population or a sample. The number of times the students on your floor order pizza in a week, ___.

Answer:

it is the answer number 1

In this case, the model that represents y as a function of x has the form of a linear equation: y=mx, we can find the value of m by following this formula:

To find the value of m, we just need to replace some pairs of x-y values from the table, for example, we can choose the points (3,196.5) and (13,851.5)

Then the equation is:

Richard initially had 1 pound of grapes. Consequently, he ate 5/8 pound of grapes and kept 3/8 pound for himself.

Richard initially had a certain amount of grapes. After consuming 5/8 pound of grapes, he had 1 1/8 pounds left. To determine the amount of grapes he ate, we can subtract what he kept from the total amount he started with.

Let's denote the total weight of grapes Richard had as "x" pounds.Richard ate 5/8 pound of grapes, so the remaining amount he kept is (1 - 5/8) pounds, which simplifies to 3/8 pound. This means 3/8 pound is equal to 1 1/8 pounds.

To find out how many pounds of grapes Richard started with, we can set up a proportion

(3/8) pounds is to (1 1/8) pounds as x pounds is to the total weight of grapes

Simplifying the proportion, we get:

3/8 = 9/8 / x

Cross-multiplying gives us:

3x = 9/8

Multiplying both sides by 8/3 gives:

x = 3/8 * 8/3 = 1

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Answer:

6/6 x 3/5, 1/4 x 3/5, 1 2/5 x 3/5, 2 x 3/5

Hope this helps

Step-by-step explanation:

Answer:

If Cora runs 1/2 mile per week and x is the number of weeks, then she will run 5+1/2x. Then determine how many weeks are in two and a half months (depends on which month it is as there are less weeks in February than in January!) but we could estimate 6.

For Hana, you will have 3+ 3/4 x First equation is y=5+1/2 x and then plug 6 in for x to solve for y. the second equation is y=3+3/4x and plug in 6.

Step-by-step explanation:

First equation is y=5+1/2 x and then plug 6 in for x to solve for y. the second equation is y=3+3/4x and plug in 6.

Answer:

9:10AM

Step-by-step explanation:

Answer: 0.1435

Step-by-step explanation:

Given : Mean = 479 pounds

Standard deviation = 40 pounds.

Let  X denote the weights of cows.

\(X\sim N(\mu=479,\sigma=40)\)

The cow transport truck holds 15 cows and can hold a maximum weight of 7350.

i.e. mean weight of cow in this case =\(\overline{x}=\dfrac{7350}{15}=490\text{ pounds}\)

If 15 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 7350 will be:-

\(P(\overline{x}>490)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{490-479}{\dfrac{40}{\sqrt{15}}})\\\\=P(z>1.065)\ \ [\because\ z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(z\leq1.065)\\\\=1- 0.8565=0.1435\ \ [\text{By z-table}]\)

Hence, If 15 cows are randomly selected from the very large herd to go on the truck,  the probability their total weight will be over the maximum allowed of 7350 = 0.1435

So, the probability their mean weight will be over 479 is \(0.53836.\)

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean.

It is given that,

\(\mu=479\\\sigma=40\\n=15\\X=maximum\ weight=7350\)

Then,

\(\bar{x}=\frac{\sum x}{n}\\ =\frac{7350}{15}\\ =490\)

Now, calculating Z-score:

\(Z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n} } } \\Z=\frac{490-479}{\frac{40}{\sqrt{15} } }\\ Z=1.07\)

Using z table =1.07

\(P(Z < 1.07)=0.46164\\P(Z > 1.07)=1-P(Z < 1.07)\\=1-0.46164\\=0.53836\)

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Answer:

Step-by-step explanation:

↘↘↘↙↙↖↗↙↖

The rate of the speeding car is 0.493.

We have,

The police car is at 80 mph and it is 44 yards from the intersection, is increasing at 45 mph, while the other car is 117 yards away from the intersection.

So, Rate of speeding car

= (45- 80)/ (117- 44)

= -35/(-73)

= 35/73

= 0.493

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To find the circumference of a circle we use the formula

according to the circle ir has a radius of 35/2m.

Insert the data in the formula and use 22/7 as the approximation of pi

Answer:

-------------------------------------------

x-intercepts, at y = 0

y-intercept, at x = 0

The base of the triangle is the distance between the x-intercepts

The height is h = - 1.5k, as it represents the distance from the x-axis

Solve the quadratic equation

1) D = 1

2) D = √17

Answer:

\(k=-2, \quad k=-1, \quad k=\dfrac{-3-\sqrt{17}}{2}, \quad k=\dfrac{-3+\sqrt{17}}{2}\)

Step-by-step explanation:

Given equation of the parabola:

\(y = 0.5(x-3)(x+k)\)

The x-intercepts are the points at which the curve crosses the x-axis.  

To find the x-intercepts, substitute y = 0 into the given equation and solve for x:

\(\implies 0.5(x-3)(x+k)=0\)

\(\implies (x-3)(x+k)=0\)

Apply the zero-product property:

\(\implies x-3=0 \implies x=3\)

\(\implies x+k=0 \implies x=-k\)

Therefore, the x-intercepts are:

The y-intercept is the point at which the curve crosses the y-axis.

To find the y-intercept, substitute x = 0 into the given equation and solve for y:

\(\implies y = 0.5(0-3)(0+k)\)

\(\implies y = 0.5(-3)(k)\)

\(\implies y = -1.5k\)

Therefore, the y-intercept is:

\(\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle} \\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height. \\\end{minipage}}\)

The height of the triangle is the distance between the y-intercept and the x-axis:

\(\implies h=-1.5k\)

The base of the triangle is the difference between the x-intercepts:

\(\implies b=3+k\quad \textsf{or} \quad b=-(3+k)\)

Given the area of the triangle is equal to 1.5 square units, substitute the values of b and h into the formula for area and solve for k:

For b = (3 + k):

\(\begin{aligned}\implies\textsf{Area}&=\dfrac{1}{2}bh\\1.5&=\dfrac{1}{2} \cdot (3+k)\cdot(-1.5k)\\-2&=(3+k)k\\k^2+3k+2&=0\\k^2+k+2k+2&=0\\k(k+1)+2(k+1)&=0\\(k+2)(k+1)&=0\\\\ k+2&=0 \implies k=-2\\k+1&=0 \implies k=-1\end{aligned}\)

For b = -(3 + k):

\(\begin{aligned}\implies\textsf{Area}&=\dfrac{1}{2}bh\\1.5&=\dfrac{1}{2} \cdot -(3+k)\cdot(-1.5k)\\-2&=-(3+k)k\\2&=(3+k)k\\k^2+3k&=2\\k^2+3k+\dfra&=4.25\\\left(k+1.5\right)^2&=4.25\\k+1.5&=\sqrt{4.25}\\k+1.5&=\pm\dfrac{\sqrt{17}}{2}\\k&=\dfrac{-3\pm\sqrt{17}}{2}\end{aligned}\)

Therefore, the possible values of k are:

\(k=-2, \quad k=-1, \quad k=\dfrac{-3-\sqrt{17}}{2}, \quad k=\dfrac{-3+\sqrt{17}}{2}\)

Answer:

Step-by-step explanation:

The volume is 8.5 gallons and this needs to be converted to litters. In this case, multiply the volume in gallons by 3.785 because each gallon contains 3.785 liters. The mass is 70 pounds and this needs to be converted to kilos. In this case, divide the pounds by 2.204 considering each kilo contains 2.204 pounds.

The length of arc RS on circle X is 17.99 centimeters.

To find the length of arc RS on circle X, we need to calculate the circumference of the entire circle and then determine what portion of the circumference is represented by the central angle of 110 degrees.

The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, the radius of circle X is 9 centimeters, so the circumference is C = 2π(9) = 18π centimeters.

To find the length of arc RS, we need to determine what fraction of the entire circumference is represented by the central angle of 110 degrees. A full circle has 360 degrees, so the fraction of the circumference represented by the central angle is 110/360.

To find the length of arc RS, we multiply the fraction of the circumference by the total circumference of the circle. Therefore, the length of arc RS is (110/360) * 18π.

Simplifying the expression, we have (110/360) * 18π = (11/36) * 18π.

Canceling out the common factors, (11/36) * 18π = (11/2)π.

Now, we can approximate the value of π as 3.14. Therefore, the length of arc RS is (11/2) * 3.14.

Calculating the approximate value, we have (11/2) * 3.14 ≈ 17.99 centimeters.

Therefore, the approximate length of arc RS on circle X is approximately 17.99 centimeters.

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Calista's grade on her last assignment is 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

To determine Calista's grade on her last assignment, we can calculate the average grade using the given information.

The sum of Calista's grades on the first five assignments is: 62 + 88 + 92 + 74 + 78 = 394.

Since the average grade is given as 82, we can find the total sum of all six assignments by multiplying the average grade by the number of assignments, which is 6: 82 * 6 = 492.

To find Calista's grade on her last assignment, we subtract the sum of her grades on the first five assignments from the total sum: 492 - 394 = 98.

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The value of x is 33.2

Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent or equal.

Also the ratio of corresponding sides of similar triangles are equal.

Therefore;

Triangle EHG and EFG are similar

39/36 = 36/x

36 × 36 = 39x

39x = 1296

divide both sides by 39

x = 1296/39

x = 33.2

Therefore the value of x is 33.2

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