A rectangular prism has a base that is 1.5 meters by 2 meters, and the prism is 4 meters
high. What is the surface area of the prism?
A 28 m
C 12 m2
B 34 m2
D 31 m²

Answer:

\(x=\frac{\sqrt{14} }{2}\)

Step-by-step explanation:

Notice that you are given an isosceles right-angle triangle to solve, since each of its two acute angles measures \(45^o\). Then such means that the sides opposite to these acute angles (the so called "legs" of this right angle triangle) must also be of the same length (x).

We can then use the Pythagorean theorem that relates the square of the hypotenuse to the addition of the squares of the triangles legs:

\((\sqrt{7})^2=x^2+x^2\\7=2\,x^2\\x^2=\frac{7}{2} \\x=+/-\sqrt{\frac{7}{2}} \\x=+/-\frac{\sqrt{14} }{2}\)

We use just the positive root, since we are looking for an actual length. then, the requested side is:

\(x=\frac{\sqrt{14} }{2}\)

Answer:

The value of x is;

Explanation:

Given the equation;

Solving for x;

Therefore, the value of x is;

Answer:

9

Step-by-step explanation:

All but 9

Answer:

12

Step-by-step explanation:

I used a calculator I hhhhhhj

The value of the equation 7/8-1/x=3/4 is 8, so x=8 is the answer.

Two or more expressions with an Equal sign is called as Equation.

The given equation is 7/8-1/x=3/4

Seven divided by eight minus one by x equal to three divided by four.

We have to find the value of x.

Minus is the operator of the equation.

7/8-1/x=3/4

7/8 -3/4 =1/x

LCM of 8 and 4 is 8

7-6 /8 = 1/x

1/8 = 1/x

So value of x is 8

Hence, the value of the equation 7/8-1/x=3/4 is 8, so x=8 is the answer.

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The greatest common factor, GCF, of 8y, -12x, and 4xy is 4

From the question, we are to determine the greatest common factor of the given expressions.

The given expressions are 8y, -12x, and 4xy

To determine the greatest common factor, we will express each of the expressions as a product of their factors.

8y = 2 × 2 × 2 × y

-12x = 2 × 2 × 3 × -x

4xy = 2 × 2 × x × y

From above, we can observe that the greatest common factor is

2 × 2

= 4

Hence, the greatest common factor is 4

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Therefore, Mr. Tompkins lives 240 miles from the airport.

Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time.

Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time.

We can start solving the problem by using the formula: distance = speed x time.

Let x be the distance from Mr. Tompkins' home to the airport in miles.

Therefore, the distance from the airport to the other city is (670 - x) miles

we know that the total traveling time is 4 hours

so we can set up two equations:

x/30 + (670 - x)/250 = 4

x + (670 - x)/8 = 120

we can solve for x

x = 240 miles

Therefore, Mr. Tompkins lives 240 miles from the airport.

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Answer:

4/25 foot²

Step-by-step explanation:

Refer to attachment*

Consider the attachment first for a better understanding, now after considering the attachment you will gotta know that, the height of the parallelogram is just same as the width of the rectangle i.e (2/5) foot and but for the base of the parallelogram we can subtract the base of one triangle from the length of the rectangle, so it will give us (3/5) - (1/25) = (2/5), so now we have breadth as well as height of the parallelogram, so now, as area of a parallelogram is given by it's height times it's base, so we will be having

\({:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{2}{5}\times \dfrac25}\)

\({:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}\)

Hence, Option D) is correct

Well, we have another method for it, we can subtract the area of both the triangles from the area of rectangle, and now,as their base of the triangle is (1/5) foot and height is same as the width of rectangle i.e (2/5) foots, so its area will be (1/2) times base times height, but as here are two triangles, so multiplying the area of one triangle by 2 will vanish 2, so now we just have

\({:\implies \quad \sf Area_{(Parallelogram)}=\bigg(\dfrac{2}{5}\times \dfrac{3}{5}\bigg)-\bigg(\dfrac{1}{5}\times \dfrac{2}{5}\bigg)}\)

\({:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{6}{25}-\dfrac{2}{25}}\)

\({:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}\)

This also, proves that the correct answer is D)

Answer:

$16.43.

Step-by-step explanation:

At the grocery store, you spent $485.72. With 2% cashback, you would get 485.72 * 0.02 = 9.7144 dollars worth of cashback.

At other places, you spend $671.28. With 1% cashback, you would get 671.28 * 0.01 = 6.7128 dollars worth of cashback.

9.7144 + 6.7128 = 16.4272, which is about $16.43 of cashback.

Hope this helps!

The amount of cashback that you earned will be $16.42.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

Suppose you earn 2% cash back at grocery stores and 1% on all other purchases. If you spent $485.72 at the grocery store and $671.28 on all other purchases.

The total cashback is calculated as,

⇒ 0.02 x $485.72 + 0.01 x $671.28

⇒ $9.71 + $6.71

⇒ $16.42

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Answer:

d

Step-by-step explanation:

You are asking a question trying to suggest whether it can be done later

Answer:

We conclude that the true average stopping distance exceeds this maximum value.

Step-by-step explanation:

We are given the following observations that are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.;

X = 32.1, 30.9, 31.6, 30.4, 31.0, 31.9.

Let \(\mu\) = true average stopping distance

So, Null Hypothesis, \(H_0\) : \(\mu \leq\) 30      {means that the true average stopping distance exceeds this maximum value}

Alternate Hypothesis, \(H_A\) : \(\mu\) > 30      {means that the true average stopping distance exceeds this maximum value}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                              T.S.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean stopping distance = \(\frac{\sum X}{n}\) = 31.32 ft

            s = sample standard deviation = \(\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }\) = 0.66 ft

            n = sample size = 6

So, the test statistics =  \(\frac{31.32-30}{\frac{0.66}{\sqrt{6} } }\)  ~  \(t_5\)

                                    =  4.898

The value of t-test statistics is 4.898.

Now, at 0.01 level of significance, the t table gives a critical value of 3.365 at 5 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of t as 4.898 > 3.365, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the true average stopping distance exceeds this maximum value.

Answer:

C.

Step-by-step explanation:

We have five unshaded, 1 half of unshaded, and 1 shaded, Thus, It will be showed as \(\frac{1}{6}\)  ➗ \(2\)

Answer:

The discount is 20% off

hope this helps!

Answer:

$203,333

Step-by-step explanation:

Computation for the break-even in sales dollars for Division Q

First step is to compute the Segment Contribution Margin ratio

Using this formula

Segment Contribution Margin ratio = Segment contribution margin ÷ Segment sales

Let plug in the formula

Segment Contribution Margin ratio= $ 175,980÷ $ 419,000

Segment Contribution Margin ratio= 0.42

Last step is to find the break-even in sales dollars for Division Q using this formula

Break-even in sales dollars = Segment traceable fixed expenses ÷ Segment Contribution Margin ratio

Let plug in the formula

Break-even in sales dollars= $85,400÷ 0.42

Break-even in sales dollars=$203,333

Therefore the break-even in sales dollars for Division Q is $203,333

Answer:

arc EFC = 237°

Step-by-step explanation:

arc DEF = 140°

arc EF = 140° - 83° = 57°

arc DC = arc FG

arc DC = (360° - 140° - 140°)/2 = 40°

arc EFC = arc CG + arc FG = arc EF = 140° + 40° + 57° = 237°

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

By using trigonometric functions, the value of \(\sin \text{x}^\circ\) is \(\frac{\text{a}}{\text{b}}\).

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.

Given

\(\sin \text{x}^\circ= \ ?\)

\(\tan \text{x}^\circ=\dfrac{\text{a}}{4}\)

\(\cos \text{x}^\circ=\dfrac{4}{\text{b}}\)

Formula to find \(\sin \text{x}^\circ\)

\(\sin \text{x}^\circ=\dfrac{\text{Opposite}}{\text{Hypotenuse}}\)

\(\rightarrow\sin \text{x}^\circ=\bold{\dfrac{a}{b}}\)

Therefore, by using trigonometric functions, the value of \(\sin \text{x}^\circ\) is \(\frac{\text{a}}{\text{b}}\).

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Answer:

2.3 hours

Step-by-step explanation:

From 3:12 pm to 4:12 pm, one hour passes.

From 4:12 pm to 5:12 pm, another hour passes.

From 5:12 pm to 5:30 pm, there are 18 minutes that pass.

Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.

To convert this to a fraction, we can write:

2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours

So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.

The expression that models the number of people attending concert 1 is given as follows:

512/6.

The number of people attending concert 1 is obtained applying the proportions in the context of the problem.

From the bar model, the fractions corresponding to each concert are given as follows:

The total number of people is given as follows:

512.

Hence the expression that models the number of people attending concert 1 is given as follows:

512/6.

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Answer:

\(m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} \)

\(7 = - \frac{8}{3} ( - 3) + b\)

\(7 = 8 + b\)

\(b = - 1\)

\(y = - \frac{8}{3} x - 1\)

The y-intercept is -1.

Answer:

250

Step-by-step explanation:

V = LWH

5 * 5 * 10 = 250

the height of a binary tree is the number of edges in the longest path from the root to a leaf.The best-case height of a binary tree with seven nodes is 3.

A binary tree is a type of tree structure consisting of nodes that are connected by edges. The number of edges in the longest path from a binary tree's root to a leaf determines the tree's height.In the best-case scenario, the binary tree is perfectly balanced and each node has exactly two children. With seven nodes, the best-case height is three because each node has two children and three edges connect the root node to the leaves. This means that the longest path from the root to a leaf is three edges, resulting in a height of three.

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Answer: 7x + 1

Step-by-step explanation:

(6x-4)+(x+5)

Step 1: Remove Parentheses:

              6x-4+x+5

Step 2: Combine Like Terms:

             7x +1

Answer:

0.028571429 or 1/35

Or if you meant 315 divided by 9 it’s 35

Step-by-step explanation:

9 ÷divided by 315 equals 0.02857 (rounded to five decimal places) or approximately 0.03.

When dividing 9 by 315, we set up the division equation: 9 ÷ 315. To perform the division, we start by dividing the first digit, 9, by the first digit of 315, which is 3. Since 3 can be divided evenly into 9, the quotient is 3.

Next, we bring down the next digit, 1, making the current dividend 15. We continue dividing 15 by 3, resulting in a quotient of 5. Finally, there are no more digits to bring down, so the division is complete.

Therefore, 9 ÷ 315 equals 0.02857 (rounded to five decimal places) or approximately 0.03.

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Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

The volume of the pyramid is 576 cubic inches.

To find the volume of a square base pyramid, you can use the formula:

Volume = (1/3) x base area x height

In this case, the side of the square base is given as 12 inches, and the height is given as 12.5 inches.

First, calculate the base area of the pyramid:

Base area = side²

= 12²

= 144 square inches

Now, substitute the values into the volume formula:

Volume = (1/3) x 144 x 12.5

Volume = 576 cubic inches

Therefore, the volume of the pyramid is 576 cubic inches.

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The true statement about the parallelogram is (c) Yes, because adjacent sides are congruent.

Given that

Figure ABCD is a parallelogram

Such that

Side lengths = 5 cm

This means that

The figure is a square

As a general rule

All squares can be classified as rhombus

This is because a rhombus is a quadrilateral with all four sides of equal length and square is a type of rhombus in which all four sides are equal in length

Hence, the true statement is (c)

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Algebraic expression for the given phrase is

\(-4+(3-1)\)

Simplified answer is -2

Given :

The given phrase is  the sum of -4 and the difference of 3 and 1

To find the difference we subtract the numbers

difference of 3 and 1 is 3-1

for the sum we add it

the sum of -4 and the difference of 3 and 1

the sum of -4 and  (3-1)

Now we add it , \(-4+(3-1)\)

Algebraic expression for the given phrase is

\(-4+(3-1)\)

Now we simplify it

\(-4+(3-1)\\-4+(2)\\-2\)

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The mean, median, range, and standard deviation  for the new data set must all be 7 greater than for the original data set.

The mean is the sum of all the values divided by the number of values. Adding the number 6 to the original data set of 30 positive integers increases the sum of all the values by 6, which means the mean for the new data set must be 7 greater than the mean for the original data set.

The formula for the mean is: Mean = (Sum of Values)/(Number of Values)

For the original data set: Mean = (Sum of Values)/30

For the new data set: Mean = (Sum of Values + 6)/31

Therefore, the mean for the new data set must be 7 greater than the mean for the original data set.

The median is the middle value in a set of data. Adding the number 6 to the original data set of 30 positive integers increases the total number of values to 31, which means the median is calculated differently for the new data set than the original data set. The median for the new data set must be 7 greater than the median for the original data set.

The formula for the median is: Median = (n+1)/2

For the original data set: Median = (30+1)/2 = 15.5

For the new data set: Median = (31+1)/2 = 16.5

Therefore, the median for the new data set must be 7 greater than the median for the original data set.

The range is calculated by subtracting the smallest value from the largest value in a data set. Adding the number 6 to the original data set of 30 positive integers increases the largest value by 6, which means the range for the new data set must be 7 greater than the range for the original data set.

The formula for the range is: Range = (Largest Value) - (Smallest Value)

For the original data set: Range = (Largest Value) - 13

For the new data set: Range = (Largest Value + 6) - 13

Therefore, the range for the new data set must be 7 greater than the range for the original data set.

The standard deviation is a measure of how spread out the values in a data set are. Adding the number 6 to the original data set of 30 positive integers increases the total number of values by 1, which means the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.

The formula for the standard deviation is: Standard Deviation = √ (Sum of (Values - Mean)2 / Number of Values)

For the original data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 30)

For the new data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 31)

Therefore, the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.

The mean, median, range, and standard deviation for the new data set must all be 7 greater than for the original data set

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