What is the surface area of the triangular prism?

Triangular prism

a
252 square feet
b
264 square feet
c
152 square feet
d
172 square feet

Answer:

see below

Step-by-step explanation:

Let x be the first integer

x+1 is the next integer

x+2 = next integer

x+3 = last integer

The sum of the 4 integers is -10

x+ x+1 + x+2  + x+3 = -10

Combine like terms

4x+6 = -10

Subtract 6 from each side

4x+6-6 = -10-6

4x = -16

Divide each side by 4

4x/4 = -16/4

x = -4

x+1 = -3

x+2 = -2

x+1  =-1

The integers are -4, -3, -2 ,-1

Answer:

Here is the answer mate. Hope it helps. Please rate my answer and mark as brainlist if you find it helpful.

Answer:

[tex] = 48 {m}^{3} [/tex]

Step-by-step explanation:

[tex]volume = l \times w \times b \\ = 1 \times 8 \times 6 \\ = 48 {m}^{3} [/tex]

Answer:  7n−13

Step-by-step explanation:

Answer: your answer is 2

Step-by-step explanation:

Answer: 3pi/5 and 5/3pi?

Step-by-step explanation:

Answer:

Step-by-step explanation:

3pi/5 * 180/pi

3/5 * 180/1

3/1 * 36

3*36

108 degrees

5/3pi * pi/180

5/3 * 1/180

1/3 * 1/36

1/108

Answer:

a shoe box

Step-by-step explanation:

i'm not 100% sure but isn't a shoe box rectangular?

Answer:

Step-by-step explanation:

The volume is the summation of the volumes of the shells. The volume of a shell is its circumference ...

  c(x) = 2πx

multiplied by its height ...

  h(x) = 5x(x -2)^2

and its thickness, dx.

That summation is the integral ...

  [tex]\displaystyle V=\int^2_0 {2\pi x(5x)(x-2)^2} \, dx=10\pi\int^2_0 {(x^2-2x)^2} \, dx=10\pi\left(\dfrac{2^5}{5}-\dfrac{4(2^4)}{4}+\dfrac{4(2^3)}{3}\right)\\\\\boxed{V=\dfrac{32\pi}{3}}[/tex]

The circumference of the shell  is c(x) = 2πx

The height of the shell is [tex]h(x) = 5x(x-2)^{2}[/tex]

The required volume of the shell is [tex]\frac{32\pi}{3}[/tex].

Given that,

S be the solid obtained by rotating the region,

Where, a = 5 and b =2

We have to determine ,

What are its circumference c and height h.

According to the question,

          c(x) = 2πx

          [tex]h(x) = 5x(x-2)^{2}[/tex]

[tex]V = \int (circumference) \ )(height )\ . dx\\\\[/tex]

Where dx thickness of the shell.

Substitute the value in the equation,

[tex]v = \int\limits^2_0 {2\pi x .(5x) (x-2)^{2} }\, dx\\\\v = \int\limits^2_0 {10\pi x^{2} (x-2)^{^{2}} \ d x\\\\\\v =10\pi \int\limits^2_0 {x^{2}.(x^2+4-4x)} \, dx \\\\V = 10\pi \int\limits^2_0( {x^{4} + 4x^{2} - 4x^{3}) \, dx[/tex]

[tex]v = 10\pi \ [ \dfrac{x^{5}}{5} + \dfrac{4x^{3}}{3} - x^{4}]^{2}_0\\\\v = 10\pi [ \dfrac{2^{5}}{5} + \dfrac{4.2^{3}}{3} - 2^{4} - \dfrac{0^{5}}{5} -\dfrac{4.0^{3}}{3} + 0^{4}]}\\\\v = 10\pi \ [ \dfrac{32}{5} + \dfrac{32}{3} - 16 -0-0+0]\\\\v = 10\pi [\dfrac{96+160-240}{15}]\\\\v = 10\pi [\dfrac{16}{15}]\\\\v = \dfrac{32\pi }{3}[/tex]

Hence, The required volume of the shell is [tex]\dfrac{32\pi}{3}[/tex].

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Answer:

a) [tex]r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857[/tex]  

The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables

b) [tex]m=\frac{64.5}{2000}=0.03225[/tex]  

Now we can find the means for x and y like this:  

[tex]\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50[/tex]  

[tex]\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425[/tex]  

[tex]b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27[/tex]  

So the line would be given by:  

[tex]y=0.3225 x -0.27[/tex]  

Step-by-step explanation:

Part a

The correlation coeffcient is given by this formula:

[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]  

For our case we have this:

n=4 [tex] \sum x = 200, \sum y = 5.37, \sum xy = 333, \sum x^2 =12000, \sum y^2 =9.3501[/tex]  

[tex]r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857[/tex]  

The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables

Part b

[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]  

Where:  

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]  

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]  

With these we can find the sums:  

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=12000-\frac{200^2}{4}=2000[/tex]  

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=333-\frac{200*5.37}{4}=64.5[/tex]  

And the slope would be:  

[tex]m=\frac{64.5}{2000}=0.03225[/tex]  

Now we can find the means for x and y like this:  

[tex]\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50[/tex]  

[tex]\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425[/tex]  

And we can find the intercept using this:  

[tex]b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27[/tex]  

So the line would be given by:  

[tex]y=0.3225 x -0.27[/tex]  

Answer:

D

Step-by-step explanation:

Answer:

there are 80 students

Step-by-step explanation:

Answer:

g(2)=11

Step-by-step explanation:

We want to find g(x), or y, when x is equal to 2. We have the equation:

g(x)=2x+7

We know that x=2, so we can substitute 2 in for x.

g(2)=2(2)+7

Multiply 2 and 2 first

g(2)=4+7

Add 4 and 7

g(2)=11

Answer:

Yes 11 is the right answer

Step-by-step explanation:

Answer:

If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit P can be expressed as:

[tex]P=3S+5H[/tex]

The restriction for cloth can be written as:

[tex]S+2H\leq500[/tex]

The restriction for metal can be written as:

[tex]2S+3H\leq600[/tex]

The restriction for wood can be written as:

[tex]4S+7H\leq800[/tex]

The condition for S and H to be positive is:

[tex]S, H \geq0[/tex]

Step-by-step explanation:

We have an objective function that, in this case, we want ot maximize.

This function is the Profit (P).

If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit can be expressed as:

[tex]P=3S+5H[/tex]

We have 3 restrictions, plus the condition that both S and H are positive.

The restriction for cloth can be written as:

[tex]S+2H\leq500[/tex]

The restriction for metal can be written as:

[tex]2S+3H\leq600[/tex]

The restriction for wood can be written as:

[tex]4S+7H\leq800[/tex]

The condition for S and H to be positive is:

[tex]S, H \geq0[/tex]

Answer:

The US civil rights movement gain new momentum after World War II as the rallying of blacks in Montgomery and Alabama by Rosa Parks. At the time black people were separated from white people. Whites were considered as a superior and high class while on the other side blacks were counted as a lower class.

Answer:

B A C

Step-by-step explanation:

It is what it is

Answer:

4 number lines. Graph A goes from 95 to 100. An open circle is at 98 and everything to the right is shaded. Graph B goes from negative 74 to negative 69. An open circle is at negative 72 and everything to the right is shaded. Graph C goes from negative 100 to negative 95. An open circle is at negative 98 and everything to the left is shaded. Graph D goes from negative 74 to negative 69. An open circle is at negative 72 and everything to the left is shaded.

Which graph is the solution to the inequality?

y - 13 > -85

13 < -85 + y

y + 13 < -85

Step-by-step explanation: edgunity!

hope this helps! :)

Answer:

[tex] Ways = 3*5*7= 105[/tex]

And that's equivalent to:

[tex] Ways= (3C1) (5C1) (7C1) =3*5*7=105[/tex]

Where C represent the term combinatory defined as:

[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]

And then the number of ways to select the three books are 105, and the best option would be:

b). 105

Step-by-step explanation:

For this case we can use the multplication principle of counting or sometimes called the product rule.

We have a total of 3 novels, 5 biographies and 7 self-help books. And we can find the number of ways that a person can select the three books with theis product:

[tex] Ways = 3*5*7= 105[/tex]

And that's equivalent to:

[tex] Ways= (3C1) (5C1) (7C1) =3*5*7=105[/tex]

Where C represent the term combinatory defined as:

[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]

And then the number of ways to select the three books are 105, and the best option would be:

b). 105

We want to see in how many different ways a person can select one book from 3 novels, one book from 5 biographies and one book from 7 self-help books, the correct option is b: 105.

To get the numbe of different ways, the first thing we need to do is find the selections.

Here we have 3 selections:

Now we need to find the number of options for each of these selections, and just multiply the numbers of options.

we have:

Number of different ways of selecting = 3*5*7 = 105

So the correct option is b.

If you want to learn more, you can read:

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Answer:

x is between 0 and 1

x is almost 0.5

y is between 2 and 3

y is almost 0.2

Answer:

1st answer: 0 and 1

2nd answer: about 0.6

3rd answer: 2 and 3

4th answer: about 2.2

Step-by-step explanation:

I got it correct! Edge 2021:)

To solve 8^2 , we have to multiply 8 with itself , this means = 8 × 8 = 64 . Thus, our answer = 8²= 64.

This also known as square of a number as we multiply it with itself .

Answer:

4%

Step-by-step explanation:

Answer:

EDITING VIEW

Step-by-step explanation:

Answer:29

Step-by-step explanation:

27r=783

   divide both sides by 27

 27r÷27=783÷27

         r=29

Answer:

[tex]r = 29[/tex]

Step-by-step explanation:

[tex]27r = 783 \\ \frac{27r}{27} = \frac{783}{27} \\ r = 29[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

400

Step-by-step explanation:

75/100 = 300/x

75x = 30000

x = 400

Answer:

2 is the answer according to me

Answer:

Step-by-step explanation:

To test the hypothesis is the mean SAT score is less than 1520 at 5% significance level

The nul hypothesis is

[tex]H_0; \mu \geq 1520[/tex]

The alternative hypothesis is

[tex]H_0 ; \mu\leq 1520[/tex]

The test statistic is

[tex]t=\frac{\bar x- \mu}{(\frac{s}{\sqrt{n} } )}[/tex]

[tex]t= \frac{1501-1520}{(\frac{53}{\sqrt{20} } )} \\\\=-1.603[/tex]

The t - test statistics is -1.603

The t - critical value is,

The small size is small and left tail test.

Look in the column headed [tex]\alpha = 0.05[/tex] and the row headed in the t - distribution table by using degree of freedom is,

d.f = n - 1

= 20 - 1

= 19

The t - critical value is -1.729

The conclusion is that the t value corresponds to sample statistics is not fall in the critical region, so the null hypothesis is not rejected at 5% level of significance.

there is insignificance evidence ti indicate that the mean SAT score is less than 1520. The result is not statistically significant

Answer:

Critical value = -1.729

Step by Step explanation:

Given:

n = 20

X' = 1501

Standard deviation = 53

Mean, u = 1520

Level of significance, a = 0.05

The null and alternative hypotheses:

H0 : u = 1520

H1 : u < 1520

This is a lower tailed test.

Degrees of freedom, df = 20 - 1 = 19

For critical value:

[tex]t critical = - t_a, _d_f [/tex]

From t table df = 19, one tailed

[tex]t critical = -t _0._0_5, _1_9 = -1.729[/tex]

Critical value = -1.729

Decision: Reject null hypothesis H0, if test statistic Z, is less than critical value.

Test statistic Z =

[tex] Z = \frac{X' - u}{\sigma / \sqrt{n}} [/tex]

[tex] Z = \frac{1501 - 1520}{53/ \sqrt{20}}= -1.603[/tex]

Z = -1.603

For p-value:

From excel,

P(t< -1.603) = t.dist( -1.603, 19, 1)

= 0.06269

≈ 0.0627

P value = 0.0627

Since test statistic Z, -1.603, is greater than critical value, -1.729, we fail to reject the null hypothesis H0.

There is not enough statistical evidence to conclude that mean is less than 1520.

Answer:

I think it’s the first and fourth

Step-by-step explanation:

Hope this helps!!!!

Answer:

Step-by-step explanation:

Volume of a triangular pyramid = 1/3 * Base area * height

Given the Base area = area of the equilateral triangle = 12/3 cm

Height of the pyramid = length of its edge = 4/3 cm

Substituting this values in the formula we have;

V = 1/3 * 12/3 * 4/3

V = 48/27

V = 16/9 cm³

The volume of the given triangular pyramid is; B: 16/3 cm²

Formula for volume of a triangular pyramid is;

V = ¹/₃ * Base area * height

We are given;

Base area = area of the equilateral triangle = 12 cm²

Height of the pyramid = length of its edge = 4/3 cm

Thus;

V =  ¹/₃ * 12 * (4/3)

V = 16/3 cm³

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Answer:

[tex]x=-3\\x=6[/tex]

Step-by-step explanation:

We begin with [tex]x^2-3x-18=0[/tex]

To factor this, we need to look for two things:

Two numbers that add together to get [tex]-3[/tex] and two numbers that multiply together to get [tex]-18[/tex].

One method to find the answer is to write out each of the solutions to the multiplication and then check the sum of each of those digits:

The numbers that multiply together to get [tex]-18[/tex] are:

1 and -18

-1 and 18

2 and -9

-2 and 9

3 and -6

-3 and 6

Now, we can add each of these pairs of digits together to find which one gives us an answer of [tex]-3[/tex]

[tex]1+(-18)=-17\\\\-1+18=17\\\\2+(-9)=-7\\\\-2+9=7\\\\3+(-6)=-3\\\\-3+6=3[/tex]

From this, we can see that 3 and -6 gave us the result of -3. This means that these are the two factors.

To get our answer from this, we need to put our answer in the form of [tex](x+a)(x+b)=0[/tex]

This gives us the factored form of [tex](x+3)(x-6)=0[/tex]

To solve this equation, we must make either parenthesis equal to zero. This means that our solutions will be

[tex]x=-3\\x=6[/tex]

By factoring, the solutions to the quadratic equation x² - 3x - 18 = 0 are x = 6 and x = -3.

To solve the quadratic equation x² - 3x - 18 = 0 by factoring, we need to find two binomials that, when multiplied, result in zero. The quadratic equation generally follows the format ax² + bx + c = 0, where a, b, and c are constants.

Here's the step-by-step process for factoring the given equation:

Step 1: Begin with the equation x² - 3x - 18 = 0.

Step 2: Identify two numbers whose product is -18 (the constant term) and whose sum is -3 (the coefficient of the x-term).

We find that the two numbers are -6 and +3 because:

-6 * 3 = -18 (the product of the two numbers is -18)

-6 + 3 = -3 (the sum of the two numbers is -3)

Step 3: Rewrite the middle term (-3x) using -6x and +3x:

x² - 6x + 3x - 18 = 0.

Step 4: Group the terms and factor them by pairs:

(x² - 6x) + (3x - 18) = 0.

Step 5: Factor out the greatest common factor from each group:

x(x - 6) + 3(x - 6) = 0.

Step 6: Notice that both terms have a common factor of (x - 6). Factor it out:

(x - 6)(x + 3) = 0.

Step 7: Apply the zero-product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero:

Setting each factor to zero and solving for x:

x - 6 = 0 --> x = 6

x + 3 = 0 --> x = -3

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Answer:

8

Step-by-step explanation:

to divide exponentials, subtract the exponents

15-x=7

x=8

Answer:

  (√55)/8

Step-by-step explanation:

The sine and cosine are related by ...

  sin² +cos² = 1

Then the sine of the angle is ...

  sin(θ₁) = √(1 -cos(θ₁)²)

  sin(θ₁) = √(1 - (3/8)²) = √(55/64)

  sin(θ₁) = (√55)/8

Answer: is answer b

Step-by-step explanation:

Answer: The answer is B

Step-by-step explanation:I did the quiz