help asap 7th grade math

The volume of the Pentagonal pyramid is 8.25 units² and surface area is 12.2 units²

A Pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces.

The volume of of a pyramid is expressed as;

V = 1/3 b × h

where b is the area of the base

Area of the base = 1/2 nsa

where s is the side length and n is the number of sides and a is the apothem.

side length = apothem × 2tan(180/n)

= √3/2 × 2tan36

= √3 × tan36

= 1.26m

Therefore,

A = 1/2( 5 × 1.26 × √3/2)

A = 1/2 ( 5.5)

A = 2.75 units²

Volume of the pyramid = 2.75 × 3

= 8.25 units²

Area of a face = 1/2bh

= 1/2 × 1.26 × 3

= 3.78/2

= 1.88 units²

Total surface area = 1.88 × 5

= 9.45 units² + 2.75units²

= 12.2 units²

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Answer:

  [tex]\sqrt[6]{2}[/tex]

Step-by-step explanation:

You want the expression 2^(2/3)/2^(1/2) in simplest radical form.

The quotient property tells you ...

  (a^b)/(a^c) = a^(b-c)

The relation between fractional exponents and roots is ...

  [tex]a^\frac{b}{c}=\sqrt[c]{a^b}[/tex]

  [tex]\dfrac{2^\frac{2}{3}}{2^\frac{1}{2}}=2^{\frac{2}{3}-\frac{1}{2}}=2^\frac{1}{6}=\boxed{\sqrt[6]{2}}[/tex]

The diameter of the circle is d = 124.73 cm

The diameter of a circle is the line that passes through the center of the circle and touches the circumference at two points.

To find the diameter of the circle, we use the formula for the area of the circle given by A = πd²/4 where d = diameter of circle

Making d subject of the formula, we have that

d = √(4A/π)

Given that the area is

substituting the values of the variables into the equation, we have that

d = √(4A/π)

d = √(4 × 98 cm²/22/7)

d = √(4 × 98 cm² × 7/22)

d = √(4 × 98 cm² × 7/22)

d = √(2744 cm²/22)

d = 124.73 cm

So, the diameter d = 124.73 cm

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Answer: $13

Step-by-step explanation:

Let x be the price of each ticket (to the aquatic show and fireworks display).

Then, we know that:

$48 = $22 + 2x

Simplifying this equation, we get:

$48 - $22 = 2x

$26 = 2x

x = $13

Therefore, the price of each ticket is $13.

The equation of the line is written as y = (2/3)x + (14/3).

The equation of a line is a mathematical representation of the relationship between each point's x and y coordinates along a straight line.

Y = mx + b, where m is the line's slope and b is its y-intercept, is its mathematical formula (the point where the line intersects the y-axis). This equation allows us to rapidly calculate the y-coordinate of a point given its x-coordinate.

The equation of the line can be written as,

y = mx + c

The slope of the line is,

m = ( y₂ - y₁) / (x₂ - x₁)

m = ( 6 - 2 ) / ( 9-3 )

m = 2/3

The y-intercept is calculated as,

y = 2/3x + c

6 = (2/3) x 2 + c

c = 14/3

The equation of the line is,

y = 2/3x + 14/3

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The probability of iii-2 and iii-3 having 2 colorblind children and 5 normal children is approximately 0.16, or 16%.

To calculate the probability of having 2 colorblind children and 5 normal children, we need to use the binomial probability formula, which is:

P(X=x) = (n choose x) x pˣ x (1-p)ⁿ⁻ˣ

where:

P(X=x) is the probability of getting k successes in n trials

(n choose k) is the binomial coefficient, which is the number of ways to choose k items from a set of n items

p is the probability of success in each trial

(1-p) is the probability of failure in each trial

x is the number of successes we want to have

In this case, we want to find the probability of having 2 colorblind children and 5 normal children, so we can plug in the values:

P(X=2) = (7 choose 2) * 0.25² * 0.75⁵

Using a calculator or computing by hand, we get:

P(X=2) = 0.16 or 16%.

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Answer:

c = 6.

Step-by-step explanation:

x^2+cx+9 = (x + b)^2     where b is a constant

x^2 + cx + 9 = x^1 + 2bx + b^2

so 2b = c

and b^2 = 9

So b = 3

and c = 2*b = 6

To solve this problem, we will use the fact that the square of a binomial (a+b)^2 is equal to a^2 + 2ab + b^2.

Let's start by assuming that x^2 + cx + 9c is the square of a binomial (a+b)^2. Expanding (a+b)^2 using the formula above, we get:

(a+b)^2 = a^2 + 2ab + b^2

If we compare this to x^2 + cx + 9c, we see that:

a^2 = x^2      (1)
2ab = cx       (2)
b^2 = 9c        (3)

From (1), we get a = ±√x^2 = ±x.

Substituting a = ±x into (2), we get:

2(±x)b = cx

Simplifying this equation, we get:

b = ±(c/2)

Substituting a = ±x and b = ±(c/2) into (3), we get:

x^2 + (c/2)^2 = 9c

Multiplying both sides by 4, we get:

4x^2 + c^2 = 36c

Rearranging this equation, we get:

4x^2 - 36c + c^2 = 0

This is a quadratic equation in c. Using the quadratic formula, we get:

c = (36 ± √(36^2 - 4(4)(c^2))) / (2(4))

Simplifying this equation, we get:

c = (9 ± √(81 - c^2)) / 2

Since c is nonzero, we can ignore the solution c = 0. Therefore, we have:

c = (9 + √(81 - c^2)) / 2   or   c = (9 - √(81 - c^2)) / 2

We can check that both solutions satisfy the original condition that x^2 + cx + 9c is the square of a binomial.

However, we need to ensure that the square root in each solution is real, which means that 81 - c^2 ≥ 0.

For the first solution, we have:

81 - c^2 ≥ 0

c^2 ≤ 81

|c| ≤ 9

Therefore, the first solution is valid for c such that -9 ≤ c ≤ 9.

For the second solution, we have:

81 - c^2 ≥ 0

c^2 ≤ 81

|c| ≥ 9

However, we already know that c is nonzero, so |c| > 0. Therefore, the second solution is not valid for any value of c.

Therefore, the only valid solution is:

c = (9 + √(81 - c^2)) / 2,   for -9 ≤ c ≤ 9.

I hope this helps! Let me know if you have any questions.
If x^2 + cx + 9c is equal to the square of a binomial, then it can be written in the form (x + A)^2, where A is a constant. Expanding the square of the binomial, we get:

(x + A)^2 = x^2 + 2Ax + A^2

Comparing this with the given expression, x^2 + cx + 9c, we can deduce the following:

2A = c and A^2 = 9c

We are asked to find the value of c. Using the first equation (2A = c), we can substitute c in the second equation:

A^2 = 9(2A)
A^2 = 18A

Since A is nonzero, we can divide both sides by A:

A = 18

Now, using the first equation, we can find the value of c:

c = 2A
c = 2(18)
c = 36

Therefore, the value of c is 36.

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The measure of the sides of the triangle is x = 15√3

Given data ,

We know that in the right triangle supplied, the bottom leg (adjacent side to the 30-degree angle) is "15" and the left leg (adjacent side to the 60-degree angle) is "x"

The ratio of the lengths of the side across from the angle and the side next to it is known as the tangent of an angle in a right triangle

From the trigonometric relations , we get

tan 60 = opposite side / adjacent side

tan(60°) = √3 = x/15

Multiply by 15 on both sides , we get

x = 15√3

Hence , the measure of side is x = 15√3

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The sum of the areas of the two squares = 104

The perimeter of the triangle is 27.67

1. We have 5x)² - x²  = 96

next wer have to solve for x

25x²  - x²  = 96

x = 2

x²  = 2²  = 4

5x)² = 10²  = 100

sum of the areas = 4 + 100 = 104

2. b = a + 4

c = b + 5

ac + bc = 2a^2 + 124

substitute b and c from the relationships:

When we simplify we have 18a = 88

a = 44/9

b = a + 4 = 44/9 + 4 = 80/9

c = b + 5 = 80/9 + 5 = 125/9

perimeter = a + b + c:

= 44/9 + 80/9 + 125/9

= 249/9 = 27.67

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Step-by-step explanation:

For a right triangle

tan Φ = opposite leg / adjacent leg

tan Φ = 40 / 630

Φ = arctan (40/630) = 3.6 degrees  

The measure you're referring to is called "Cohen's d." It expresses the difference between the experimental and control group in standard deviation units, providing an indicator of effect size and meaningfulness in a study.

The measure of meaningfulness that expresses the difference between the experimental and control group in standard deviation units is the effect size. Effect size is typically calculated by dividing the difference between the means of the two groups by the standard deviation of the control group. It is a useful tool for comparing the effectiveness of different interventions or treatments, as it allows researchers to assess the magnitude of the difference between the groups beyond just statistical significance.

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The proper way to determine the seat width of a wheelchair for an individual is to measure the widest aspect of their hips or thighs, and then add approximately 2 inches to that measurement to determine the minimum seat width.

The extra 2 inches are required to allow for comfortable placement, movement, and sitting in the wheelchair. It's crucial to remember that this serves only as a basic guideline and that the actual seat width needed may change based on the demands and preferences of the individual.

For instance, people with particular medical issues or disabilities could need seats that are larger or narrower than average. Therefore, it is advised that a healthcare professional be consulted to help identify the best seat width for a particular person, such as an occupational therapist or physical therapist.

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The expected value 'w' for the total raffle tickets sold for $1.00 with other conditions is equal to $0.784.

Number of raffle tickets sold for $1.00 = 2000

Expected value of w is ,

= Expected value of the prize won - cost of a single ticket $1.00

The probability of winning a $25 prize is

=  20/2000

= 0.01.

The expected value of winning this prize is equal to

= (25 - 1) × 0.01

= 0.24

The probability of winning a $50 prize is

= 10/2000

= 0.005.

The expected value of winning this prize is equal to

=  (50 - 1) × 0.005

= 0.245

The probability of winning a $300 prize is

= 2/2000

= 0.001.

The expected value of winning this prize is,

= (300 - 1) × 0.001

= 0.299

This implies,

The expected value of w is equal to

= 0.24 + 0.245 + 0.299

= 0.784

Therefore, the expected value of winning a prize minus the cost of the ticket is $0.784.

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The least amount of ratings the particular company can receive is 3 on the seventh survey and still be eligible to have an average of at least 8 for the first 10 surveys.

Here we have to implement basic algebraic application
Let us consider x as the  the least rating the company can get on the seventh survey.
The average of the first six surveys is 7.7, so their total score is 6 × 7.7 = 46.2.

The average of at least 8 for the first ten surveys, their total score should be at least 80.
So for the first ten surveys, their total score should be
80 = (46.2 + x + y)/10
Here
y = score for survey 8 and survey 9.

Evaluating for y
y = (80 - 46.2 - x × 2)/2
= (33.8 - x)/2.

As  each survey rating is an integer between 0 and 10 inclusive, we need to find the smallest integer value of x that makes y ≥ 0

Then, (33.8 - x)/2 >= 0.
Multiplying both sides by 2
33.8 - x >= 0
Subtracting 33.8 from both sides
-x >= -33.8
Multiplying both sides by -1
x <= 33.8
Hence, the smallest integer value of x that makes y ≥0 is x = 3.

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Answer:

The answer is 29/35

Step-by-step explanation:

2/5+3/7

find the LCM of 5 and 7

[7(2)+5(3)]/35

14+15/35=29/35

The sample size required if we wish to develop a 90% confidence interval for the average diameter is more than 0.1 units. 

To decide the test estimate required for a 90% certainty interim for the normal distance across, we have to know the taking after :

1. The level of certainty (which is 90% in this case).

2. The standard deviation of the populace (which we'll expect is known).

3. The margin of error (which is the greatest separation between the test cruel and the genuine populace cruel that we're willing to endure).

Assuming we know the standard deviation of the populace, ready to utilize the equation:

n = (z²* σ²) / E²

where:

n is the test measure

z is the z-score compared to the level of certainty (which is 1.645 for 90% certainty)

σ is the standard deviation of the populace

E is the edge of mistake

We ought to select esteem for E, which speaks to the most extreme separation between the test cruel and the genuine populace cruel(mean) that we're willing to endure.

For case, in the event that we need the interim to have a width of no more than 0.1 units, at that point we would select E = 0.1/2 = 0.05.

So, stopping within the values we know, we get:

n = (1.645² * σ²) / E²

In case we accept that the standard deviation of the populace is 0.5 units (fair as a case), at that point we get:

n = (1.645² * 0.5²) / 0.05²

n = 67.65

Adjusting up to the closest numbers, we would require a test estimate of 68 to create a 90% confidence interim for the normal breadth with an edge of blunder of no more than 0.1 units. 

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Triangle QRT with coordinates Q(-2,-1), R(1,5), and T(-8,-4) is a scalene triangle.

To classify the triangle QRT by its sides, we need to find the lengths of its three sides and compare them. We can use the distance formula to calculate the length of each side

The length of RT = √[(1 - (-8))² + (5 - (-4))²] = √[9² + 9²]

= √[162]

= 9√(2) units

The length of QT = √[(-8 - (-2))² + (-4 - (-1))²]

= √[(-6)² + (-3)²]

= √[45]

= 3√(5) units

The length of QR = √[(1 - (-2))² + (5 - (-1))²]

= √[3² + 6²]

= √[45]

= 3√(5)

Since all three sides have different lengths, triangle QRT is scalene

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The given question is incomplete, the complete question is:

Given the coordinates, classify triangle QRT by its sides. Q(-2, -1), R(1,5), T(-8,-4)

Answer:

Subtract 142 from 180 since angle of a straight line adds upto 180 degrees..

Ans will be =38

Answer:

We can rewrite the given expressions as:

(3x² - y² - 2yz - z²) and (y² - z² - 2zx - x²)

To find the H.C.F., we can use the Euclidean algorithm. We start by dividing the first expression by the second expression:

(3x² - y² - 2yz - z²) ÷ (y² - z² - 2zx - x²)

Using long division or synthetic division, we get:

(3x² - y² - 2yz - z²) = (3x + y + z)(x - y + z) + 2y(x - z)

Therefore, the remainder is 2y(x - z). We can now divide the second expression by this remainder:

(y² - z² - 2zx - x²) ÷ 2y(x - z)

Using long division or synthetic division, we get:

(y² - z² - 2zx - x²) = -x(x - y + z) + z(x - y + z)

Therefore, the remainder is z(x - y + z).

Since the second remainder is not zero, we need to continue with the algorithm. Now we divide the remainder 2y(x - z) by the remainder z(x - y + z):

2y(x - z) ÷ z(x - y + z)

Using long division or synthetic division, we get:

2y(x - z) = 2y(x - y + z) - 2y²

Therefore, the remainder is -2y². Now we divide the previous remainder z(x - y + z) by this new remainder:

z(x - y + z) ÷ (-2y²)

Using long division or synthetic division, we get:

z(x - y + z) = -1(-2y²) + z²

Therefore, the H.C.F. of the original expressions is the absolute value of the last remainder, which is |-2y²| = 2y².

Therefore, the H.C.F. of (3x² - y² - 2yz - z²) and (y² - z² - 2zx - x²) is 2y².

The null hypothesis (H0) is that the average delivery time for U.S. packages during December is 2 days, while the alternative hypothesis (Ha) is that the average delivery time is longer than 2 days.

Based on your question, you want to test if the average delivery time for U.S. packages in December is longer than 2 days. In this hypothesis test, you would have the following hypotheses:

Null Hypothesis (H0): The average delivery time for U.S. packages in December is 2 days.
Alternative Hypothesis (H1): The average delivery time for U.S. packages in December is greater than 2 days.

Thus, H0: μ ≤ 2 (where μ is the population mean delivery time)
Ha: μ > 2

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Answer:

Above picture is,

the explanation.

Answer:

x= (2010/(c+12)) +25

Step-by-step explanation:

2010= (x-25) (c+12)

x-25 = 2010/(c+12)

x= (2010/(c+12)) +25

A graph of the given quadratic equation is shown below.

The axis of symmetry is equal to 3.

The vertex is equal to (3, -1).

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function y = x² - 6x + 8 is positive 1, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -1.

In conclusion, the axis of symmetry is 3 while the vertex is given by the ordered pair (3, -1).

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Answer:      B

Step-by-step explanation:

It is speeding up

Answer:

x=18.75

Step-by-step explanation.

We have to realize that this is a line. A line has 180 degrees.

Therefore we can make the equation;

(6x+30)+2x=180

8x+30=180

8x=150

x=18.75

please mark as branliest

Answer:

x=18.75

Step-by-step explanation:

We can see that these 2 angles are on a straight line, meaning that these 2 angles must add up to 180°.

We can set up an equation:

180=(6x+30)+2x

combine like terms

180=8x+30

subtract 30 from both sides

150=8x

divide both sides by 8

x=18.75

Hope this helps! :)

The graph of the data set is in the image at the end, and it can be modeled by the quadratic:

y = 2*(x + 1)² - 3

Here we have the table:

x            y

-2,         -1

-1,          -3

0,           -1

1,             2

2,            7

The graph of it can be seen in the image at the end, there we can see that this seems to be a quadratic function

At the graph we also can see that (-1, -3) is te vertex, then if the leading coefficient is a, we can write the quadratic equation as:

y = a*(x + 1)² - 3

And we know that the equation passes throug (0, -1), replacing that we will get.

-1 = a*(0 + 1)² - 3

-1 = a - 3

-1 + 3 = a

2 = a

The function is:

y = 2*(x + 1)² - 3

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The equation "14 + 5x -11 = 7x + 3 - 2x" has infinitely many solutions, so any value of "x" will satisfy the equation.

In order to solve for "x" in the equation "14 + 5x - 11 = 7x + 3 - 2x", we need to simplify the expression by combining like terms:

14 + 5x - 11 = 7x + 3 - 2x

Simplifying the LHS,

We get,

3 + 5x = 7x + 3 - 2x

Simplifying the RHS,

We get,

3 + 5x = 5x + 3

Subtracting 5x from both sides,

We get,

3 = 3

The equation simplifies to 3 = 3, which is always true.

This means that the equation has infinitely many solutions and that any value of "x" will satisfy the equation.

Therefore, there is no unique value of "x" that can be found from the equation.

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The given question is incomplete, the complete question is

Find the value of "x" in the expression "14+5x -11= 7x+3-2x".

To decrease the type II error in a hypothesis test while maintaining the type I error at its current level, we need to increase the sample size.

Type I error shows when we reject a null hypothesis which is actually true. Type II error shows when we fail to reject a null hypothesis which is actually false.

Increasing the sample size can decrease the probability of making a Type II error, as it increases the power of the hypothesis test. Probability of correctly rejecting a false null hypothesis is called power.

By increasing the sample size, we can increase the power of the test while maintaining the significance level (and thus the type I error) at its current level.

This means that we will be less likely to miss a true effect (i.e., lower the probability of making a Type II error) while still controlling the probability of false positives (i.e., Type I error) at the desired level.

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Answer:

R93,750. (I have changed R to $ in explanation)

Step-by-step explanation:

To determine the cost of the car inclusive of VAT, trade-in, and other fees, we first need to calculate the VAT amount. Assuming the VAT rate is 15%:

VAT = 0.15 x $75,000 = $11,250

Next, we can calculate the total cost of the car, inclusive of VAT:

Total cost of car = Cost of car + VAT

Total cost of car = $75,000 + $11,250

Total cost of car = $86,250

We also need to take into account the trade-in and the other fees. The trade-in value of $9,500 and the other fees of $2,000 are subtracted from the total cost of the car:

Total cost of car inclusive of VAT and other fees = Total cost of car + Trade-in value - Other fees

Total cost of car inclusive of VAT and other fees = $86,250 + $9,500 - $2,000

Total cost of car inclusive of VAT and other fees = $93,750

Therefore, the cost of the car, inclusive of VAT, trade-in, and other fees, is $93,750.