Choose the correct answer in each number.

1. It is the sum of all areas of lateral faces
and bases of solid figure.
A. Base area B. Lateral area C. Surface area D. None of the above

2. A flat pattern that you can fold to form a solid figure is called a/an _____.
A. Area B. Edge C. Face D. Net

3. The surface area of a cube is _____ times the area of its face.
A. Three B. Four C. Five D. Six

4. In a cylinder, the edge or length of the lateral surface is equal to _____ of its base.
A. Circumference B. Perimeter C. Radius D. All of the above

5. The lateral surface of a cylinder when it is unrolled will be _____
A. Rectangle B. Trapezoid C. Triangle D. All of the above

6. The solid figure that has surface area equivalent to for times the areas of circles of the same radii is _____.
A. Cube B. Cone C. Tetrahedron D. Sphere

7. To get the lateral area of a cone, we use the formula _____.
A. L.A.=πr2 B. L.A.=πrs C. L.A.=πrh D. L.A.=rh

8. The sum of the area of the square base and four triangular lateral faces is the surface area of _____.
A. Cube B. Rectangular prism C. Pyramid D. Cone

9. The unit for surface area is _____.
A. Cubic unit B. Linear unit C. Square unit D. Weight unit

10. A cone has a radius of 5 cm and slant height of 7.1 cm. What is the unit of measure appreciate for its surface area?
A. Square milimiter (mm2) B. Square centimeter (cm2) C. Square decimeter (dm2) D. Square meter (m2)​

The classification of the system of linear equations 4x + y = 4 and y = -4x + 4 is: consistent and independent. The Option B is correct.

We have a consistent independent equation when a system of linear equations has exactly one solution. When this occurs, the graphs of the system's lines cross at exactly one point.

For our question, we can start by rearranging the first equation to isolate y:

\(4x + y = 4\\y = -4x + 4\)

We can see that the second equation is already in the form y = mx + b, where m is the slope and b is the y-intercept. So we can identify that the slope of the second equation is -4 and the y-intercept is 4.

Now we can compare the slopes and y-intercepts of the two equations to determine the classification of the system of equations:

In this case, we can see that the slopes of the two equations are different (-4 and 0) and the y-intercepts are the same (4). Therefore, the system is consistent and there is a unique solution. So the classification of the system of linear equations 4x + y = 4 and y = -4x + 4 is: consistent and independent

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Independent variables are the factors that are manipulated or controlled by the researcher in a study. In the context of investigating the impact of a school nutrition program on grade performance of high school students, the independent variable would be the school nutrition program itself.

The researcher would design and implement the program, and this variable would be under their control.

Dependent variables, on the other hand, are the outcomes or variables that are measured in a study and are expected to change as a result of the independent variable. In this case, the dependent variable would be the grade performance of the students. The researcher would collect data on the grades of the students before and after the implementation of the nutrition program, and this would be the variable that is expected to be influenced by the independent variable.

In summary, the independent variable in this research design is the school nutrition program, while the dependent variable is the grade performance of the students. The researcher would manipulate the independent variable (implement the nutrition program) and then measure the dependent variable (student grades) to determine if there is an impact of the program on grade performance.

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Answer:

1440°

Step-by-step explanation:

Each exterior angle of a 10 sided regular polygon =360/10=36°  

Each interior angle = 180°-36° =144°.  

Sum of all interior angles = 144°×10. = 1440°.

A quadratic equation in one unknown;

has two roots. In order to determine these roots, we need to apply certain operations. We can get information about the existence of these roots by discrimination. Below is the discrimination formula.

If we apply discriminant for the above equation, we obtain the following expression;

If the discriminant number is greater than \(0\), the equation has two real and distinct roots.

Now let's remember our formula for finding the roots and solve the problem using the discriminant value.

Therefore;

Other root is;

Based on the given information, the null and alternative hypotheses are not specified, making it impossible to determine whether to reject the null hypothesis or not without additional calculations and analysis.

The null and alternative hypotheses for this test would be:

Null hypothesis (H0): The proportion of people who own cats is equal to 80%.

Alternative hypothesis (Ha): The proportion of people who own cats is significantly different than 80%.

The test is a two-tailed test because the alternative hypothesis is not specific about the direction of the difference.

Based on the given information, a random sample of 400 people was taken, and 88% of the sample owned cats. The test is conducted at the 0.01 significance level.

To determine whether to reject the null hypothesis, we would perform a hypothesis test using appropriate statistical methods. The conclusion about rejecting or not rejecting the null hypothesis would depend on the test statistic and its corresponding p-value.

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Explanation

Step 1

The middle number is 6 and the last number is -7.

Factoring means we want something like

We need two numbers that...

Add together to get 6

Multiply together to get -7

c

By using probability, it can be calculated that

Probability that when two balls are selected at random with no replacement , both are green = 0.357

What is probability?

At first it is important to know about probability of an event.

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Number of green balls = 5

Number of red balls = 3

Total number of balls = 5 + 3 = 8

Probability that when two balls are selected at random with no replacement , both are green = \(\frac{5}{8} \times \frac{4}{7} = \frac{5}{14} = 0.357\)

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Answer:

THE ANSWER IS =49

Step-by-step explanation:

PLEASE FOLLOW ME ON BRANIY

Maybe Answer: It may be -1 but I am not sure, sorry!

Answer:

x = 3, y = 2

Step-by-step explanation:

~ Through process of elimination ~

1.         - 8x + 2y = -20      

        +   8x - 5y = 14

2. Simplify to solve for y through simple algebra:

          2y - 5y = -20 + 14 ⇒ - 3y = - 6 ⇒ y = 2

3. Now substitute this value of y into the to equation - 8x + 2y = -20 to get x:

- 8x + 2 ( 2 ) = -20  ⇒

    -8x + 4 = -20 ⇒

       -8x = -24 ⇒

           x = 3

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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The digits in millions period of the number is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.

Given the number is 21,468,127,471.

The digits in which are given in the large numbers are in groups of three places. The groups are called periods. Commas are usually used to separate the periods.

The groups of numbers are 3 digit group and which is starting from the right to left.

As we all know that we read the group of periods as ones, tens, hundreds, thousand, ten thousand, hundred thousand, million, ten million, hundred million, billion etc.

From  the above, we find that the given number 21,468,127,471 contains digit 1 is in the ones place, 7 is in the tens place, 4 is in the hundredth place, 7 is in the thousand place, 2 is in the ten thousand place, 1 is in the hundred thousand place, 8 is in the million place, 6 is in the ten million place, 4 is in the hundred million place , 1 is the billion place and 2 is in the ten bilion.

Hence, the digits in millions period of the given number 21,468,127,471 is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.

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Nate and lane share a 18-ounce bucket of clay. by the end of the week, Nate has used 1 6 of the bucket, and lane has used 2 3 of the bucket of clay. Therefore, there are 3 ounces of clay left in the bucket.

To find the number of ounces left in the bucket, we need to subtract the amounts used by Nate and Lane from the total capacity of the bucket.

Nate has used 1/6 of the bucket, which is (1/6) * 18 ounces = 3 ounces.

Lane has used 2/3 of the bucket, which is (2/3) * 18 ounces = 12 ounces.

To find the remaining clay in the bucket, we subtract the total amount used from the total capacity:

Remaining clay = Total capacity - Amount used

Remaining clay = 18 ounces - (3 ounces + 12 ounces)

Remaining clay = 18 ounces - 15 ounces

Remaining clay = 3 ounces

Therefore, there are 3 ounces of clay left in the bucket.

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Answer:

Simply -95.75

Step-by-step explanation:

3/4 or 3 ÷ 4= 0.75

-95 + -0.75 = -95.75

Answer:to answer this question you have to look at what the relationship is between tones of sugar and the equation C(n) = 6,500 + 225n. The question gave you a hint in parenthesis in the form of (n) tons. This statement means that the amount of sugar is n so for question 1 the 13 tons is the n value.

Q1:

C(13) = 6,500 + 225*13

C(13) = 6,500 + 2,925

C(13) = 9,425

so what does the 9,425 mean? This is the cost to transport 13 tons of sugar.

Q2:

so this part n is unknown and we are given the C(n) number.

11,450 = 6,500 + 225n

subtract the 6500 from both sides

11,450 - 6,500 = 225n

evaluate

4,950 = 225n

I don't like the n on the right side so I am going to rewrite the equation

225n = 4,950

divide by 225

n = 4,950/225

evaluate

n = 22

So this result means that the company would transport 22 tones of sugar.

Have a great day!

Step-by-step explanation:

The formula for Permutation is,

The expression given is,

Given:

Plug in n = 9, r = 4

Simplify

Hence, the answer is 3,024.

Answer:

13x = 39

x=3

y=10

Answer:

Timespan is 1 hour(s) and 35 minute(s).

Step-by-step explanation:

Hope this helps

Answer:

rip

Step-by-step explanation:

Answer:

#1 is Geometric

the common ratio is 2

#2 is Arithmetic

the common difference is 6

Answer:

There are no possible real values for x.

Step-by-step explanation:

The equation states:

4-x²>10

-x²>10-4 (Move 4 to the other side)

-x²>6 (Multiplying by -1 changes the sign)

x²<-6

In the case that we aren't working with imaginary numbers, no number squared would give -6, or anything below -6.

Hope this helps, and let me know if imaginary numbers are necessary for this question ♡

The surface area of each face is 4 square inches.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A regular octahedron has a surface area of 32 square inches.

That means

all sides are equal.

The surface area of each face is,

= 32/8

= 4 square inches.

Therefore, the required area is 4 square inches.

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The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

Step-by-step explanation:

smallest: 21

medium: 72

Large: 87

Triangles always add up to 180. Subtract the 87 and 21 from the 180 and you get the missing size.

Have a good day

Answer: The first one: 6^-6

Step-by-step explanation:

When you convert all of them to decimals the original and the first one have the same decimal.

Given function is, f(s) = (s² +65 +1)To find the derivative with respect to x of f(x),

first replace s with x and then differentiate the function.

Hence, f(x) = (x + 4) + Xx+4) + (x+4)² +2= x + 4 + x² + 4x + x² + 8x + 16 + 2= 2x² + 12x + 22

Differentiating with respect to x, we getf'(x) = 4x + 12

Given function is, f(x) = ((8x³ + 6)*¹ + 3)² + 9 Taking the derivative of f(x) with respect to x, we get:

f'(x) = 2 ((8x³ + 6)*¹ + 3) * ((8x³ + 6)¹ + 3)' + 0= 2 (8x³ + 6) * 24x²= 48x² (8x³ + 6)

To find the derivative with respect to u of g(u) = √8u+8,

we first rewrite g(u) as:

g(u) = (8u+8)¹/²

Taking the derivative of g(u) with respect to u, we get:

g'(u) = ½ (8u+8)-½ * 8= 4 (8u+8)-½= 4 / √8u+8

Hence, the derivative with respect to x of f(x) = 2x² + 12x + 22 is f'(x) = 4x + 12.

The derivative with respect to x of f(x) = ((8x³ + 6)*¹ + 3)² + 9 is f'(x) = 48x² (8x³ + 6).

The derivative with respect to u of g(u) = √8u+8 is g'(u) = 4 / √8u+8.

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Using the chain rule ,derivative of function is f'(s) = 2xf'(x) = 2x + 5f'(x) = 48x²(8x³ + 9)²d/dx [g(u)] = 4/√(8u + 8)

Given function f(s) = (s² + 65 + 1).

To find the derivative of f(x) with respect to x:

f(s) = (s² + 65 + 1)ds/dx = 2s

{Derivative of s²}ds/dx

= 2xdx/dsdx/ds

= (2x)/2sx/ ds

= x/sf'(s)

= df/ds * ds/dx

where, df/ds = 2s and ds/dx = x/sf'(s) = 2s * (x/s) = 2x

To find the derivative of f(x) with respect to x:

f(x) = (x + 4) + x(x + 4) + (x + 4)² + 2

To differentiate the given function with respect to x, we'll first simplify the expression by expanding (x+4)²f(x) = x + 4 + x² + 4x + 16 + 2f(x) = x² + 5x + 22d/dx [f(x)] = d/dx [x²] + d/dx [5x] + d/dx [22]d/dx [f(x)] = 2x + 5

Therefore, f'(x) = 2x + 5

To find the derivative of f(x) with respect to x:

f(x) = ((8x³ + 6)*¹ + 3)² + 9

To differentiate the given function with respect to x,

we'll first simplify the expression

f(x) = (8x³ + 6 + 3)² + 9f(x) = (8x³ + 9)² + 9d/dx

[f(x)] = d/dx [(8x³ + 9)²] + d/dx [9]

Using the chain rule, we can differentiate f(x) with respect to x:

d/dx [(8x³ + 9)²] = 2(8x³ + 9) * d/dx [8x³ + 9]d/dx [8x³ + 9]

= 24x²

Therefore,

d/dx [(8x³ + 9)²] = 2(8x³ + 9) * 24x²

= 48x²(8x³ + 9)²d/dx [f(x)]

= 48x²(8x³ + 9)² + 0

d/dx [f(x)] = 48x²(8x³ + 9)²

To find g'(u) given g(u) = √8u + 8.

d/dx [g(u)] = d/du [g(u)] * d/dx[u]d/dx[u] = 1

Using the chain rule,d/dx [g(u)] = 1/2(8u + 8)-1/2 * 8d/dx [g(u)] = 4/√(8u + 8)

Final answer:f'(s) = 2x

f'(x) = 2x + 5

f'(x) = 48x²(8x³ + 9)²

d/dx [g(u)] = 4/√(8u + 8)

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