A triangular prism has the
dimensions as shown below.
Each congruent base is an
equilateral triangle.
24.2 mm
28 mm
40 mm
Which of the following
measurements is closest to the
total surface area of the
triangular prism in square
millimeters?

Answer: 75% percentage grade i think

From (1) solve for x:

From (2) solve for x:

the solution is:

By converting the equation 3x - y = 7 in the slope-intercept form, the slope, and the intercept will be (A) m = 3, b = -7.

When you know the slope of the line to be investigated and the given point is also the y-intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b).

The y value of the y-intercept point is denoted by the symbol b in the formula.

A line's slope and y-intercept are expressed in the following formula: y=mx+b.

The y-intercept, which is usually represented in coordinate form as (0,b), is the point where the line crosses the y-axis.

So, we have the equation:

3x - y = 7

After reading the above-given description about the slope-intercept form, we can tell that in the given equation:
m = 3, b = -7

Therefore, by converting the equation 3x - y = 7 in the slope-intercept form, the slope and the intercept will be (A) m = 3, b = -7.

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Complete question:
After 3x - y = 7 is put in slope-intercept form, the slope, and intercept are:

a m = 3, b = -7

b m = -3, b = 7

c m = -3, b = -7

d m = 3, b = 7

The option that best describes the change in viewers the network is experiencing is B. Each year, the total number of viewers increases to approximately 120% of the previous year's total.

When 't' surpasses 1/ln(5) at 3.5, the expression yields a negative result; connoting the network is witnessing a dwindling viewership.

Consequently, the network initially experiences an intensifying viewership ratio which then fades; in accordance with Option B, "Each year, the total number of viewers increases to roughly 120% of the preceding year's sum". Clearly, this demarcation reveals itself as the accurate answer.

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Answer:

1 lb

Step-by-step explanation:

Picked up 3/5 and 4/5.

Used 3/8.

Amount now:

3/5 + 4/5 - 3/8 =

= 7/5 - 3/8

= 56/40 - 15/40

= 41/40

Answer: 1 lb

Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.

What is differentiation?

In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.

Main body:

by using product rule;

Let = u = x² + 4x + 6

⇒ du/dx = 2x + 4 .

Now y = u⁵

⇒ dy/dx = 5u⁴ .

dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)

= 5 * (x² + 4x + 6)⁴ * (2x + 4)

= 5(2x + 4) * (x² + 4x + 6)⁴

hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.

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The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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The smallest positive integer n such that t \($\sqrt[4]{56 \cdot n}$\)  is an integer is 686.

We have to find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer

To find the smallest positive integer n such that  \($\sqrt[4]{56 \cdot n}$\)   is an integer, we need to determine the factors of 56 and find the smallest value of n that, when multiplied by 56, results in a perfect fourth power.

The prime factorization of 56 is:

56 = 2³ × 7

The prime factors of 56 need to be raised to multiples of 4.

Therefore, we need to determine the smallest value of n that includes additional factors of 2 and 7.

To make the expression a perfect fourth power, we need to raise 2 and 7 to the power of 4, which is 2⁴ × 7⁴

The smallest value of n that satisfies this condition is:

n = 2 × 7³ = 2× 343 = 686

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Answer:

y = 9x + 10

Step-by-step explanation:

y = mx + b

Here, m is slope and b is y-intercept

y = 9x + 10

Answer: f(x)

Step-by-step explanation:

Answer:

0.75

Step-by-step explanation:

there is 1000 grams in 1 kilogram so I divided 750 by 1000 to get 0.75.

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Thus, the value of x is 1.

The description that will be used to break this problem is D description of a midpoint.

By description, a midpoint is a point on a line member that divides it into two equal corridor. thus, Y is the midpoint of XZ, which means that XY is equal in length to YZ.

Using the Member Addition hypothetical( A), we can write

XZ = XY YZ

Substituting the values given in the problem, we get

x- 2 = XY 2x 2

Simplifying this equation, we get

x- 2 = XY 2x 2

4x = 4

x = 1

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It should be (A).

$12.50

If you use this specific formula; 500(1+(0.30)/(12))^(1) then you calculate it you get 512.5

Then you subtract 512.5 from 500 and get your answer.

The interest she needs to pay if she pays within 1 months with no previous balance is $12.50. Option A is the correct answer.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

The compound interest is given as:

\(A = P(1 + \frac{r}{n} )^{t}\)

Where, P is the principal amount = $500.

r is the rate = 30% = 0.3

n = number of times interest is compounded = 12

t = time = 1

Substituting the value:

\(A= 500(1 + \frac{0.30}{12} )^1\)

A = 512.5

The interest is:

I = 512.5 - 500

I = 12.50

Hence, the interest she needs to pay if she pays within 1 months is $12.50. Option A is the correct answer.

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Lihle would need 30 liters of milk to make 120 cupcakes.

To determine the amount of milk Lihle needs to make 120 cupcakes, we can calculate the total milk requirement by multiplying the milk quantity per cupcake by the number of cupcakes.

Given that the recipe requires 250 milliliters (ml) of milk per cupcake, we can proceed with the calculation:

Convert milliliters to liters:

Since there are 1,000 milliliters in a liter, we divide 250 ml by 1,000 to get the milk quantity per cupcake in liters, which is 0.25 liters.

Multiply the milk quantity per cupcake by the total number of cupcakes: Multiply 0.25 liters (milk per cupcake) by 120 cupcakes.

0.25 liters/cupcake \(\times\) 120 cupcakes = 30 liters.

Therefore, Lihle would need 30 liters of milk to make 120 cupcakes in a US curriculum class.

It's important to note that this calculation assumes the given milk requirement of 250 milliliters per cupcake and does not consider any other ingredients or variations in the recipe.

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The complete question may be like: Assuming that the recipe requires 250 milliliters (ml) of milk per cupcake, how many liters of milk does Lihle need to make 120 cupcakes in a US curriculum class?

The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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Answer:

33

hope this helped :)

Answer:

I think it's 8 - ab but I'm not really sure

Answer:

Below

Step-by-step explanation:

(25380 - 18000) / 18000     * 100% =

7380/18000 * 100 = 41 % increase

In this case, I = -$13,863 million. The negative sign indicates a loss or negative income for the company.

A corporation is said to be in a net income loss, sometimes known as a net loss, when its expenses outweigh its income or revenues. It is the outcome that is negative after all costs, such as operational costs, taxes, interest, and other charges have been subtracted from the total income obtained for a given time period usually a fiscal year.

If the net income loss for the fiscal year 2016 is given as $13,863 million, we can assign this value to the variable I, which represents the income in millions of dollars.

Therefore, in this case, I = -$13,863 million. The negative sign indicates a loss or negative income for the company.

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Answer:c, the answer is c

Step-by-step explanation:

The steps for bisecting a line segment are to place the reflective device, draw the line of reflection, place the reflective device on point B, move the reflective device around, place the reflective device on point A and repeat the process.

This process implies creating a new line that is perpendicular to the original line, which means the new line will cross the original one. The steps for this are:

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Answer:

28 students

Step-by-step explanation:

Work backwards.

First, subtract 3:

115 - 3 = 112

Then, divide by 4:

112 ÷ 4 = 28

So, there are 28 math students in his class.

The product of the expression 7 x 63 is 441.

We have,

To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:

7 x 63 = 7 x (60 + 3)

Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:

7 x (60 + 3) = 7 x 60 + 7 x 3

Simplifying further:

7 x 60 + 7 x 3 = 420 + 21

Therefore,

The product of 7 x 63 is 441.

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The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

hmmmmm

Step-by-step explanation:

Answer:

∠3 = 108

Step-by-step explanation:

∠1 + ∠2=180 because a straight line is 180°

∠1=5x+10  and  ∠2=9x+2

5x+10  +  9x+2 = 14x+12

14x+12=180

180-12=168

168/14=12

x=12

∠2 = 9x+2 = 110

180-110 = 70

∠4 = 70

∠4 + ∠3 + ∠5 = 180

∠5 = 90 -5x = 30

i messed up the process here lol but the answer is for sure right

The dilatiοn preserves the side lengths and angles οf triangle. The reflectiοn dοes nοt preserve side lengths and angles.

A geοmetrical adjustment that changes an οbject's size is dilatiοn. In mοre detail, dilatiοn entails extending οr cοntracting an item by increasing each pοint's distance frοm a fixed center pοint by a predetermined amοunt, knοwn as the scale factοr.

Let's start by applying the reflectiοn alοng the y-axis. All οf the vertices will have their x-cοοrdinates negated as a result, but their y-cοοrdinates will remain unchanged.

After reflectiοn, pοint A (-4, -2) will appear as A'. (4, -2). In the same way, B (-4, -2) will becοme B' (-4, -2), and C (4, -4) will change intο C'. (-4, 4).

Applying a dilatatiοn by a factοr οf 1/2 with the οrigin as the center will cοme next. This will result in a halving οf all distances frοm the οrigin.

After dilatiοn, pοint A' (4, -2)'s image will be A'' (2, -1), B' (-4, -2) will change tο B'' (-2, -1), and C' (-4, -4) will becοme C''. (-2, 2).

We must cοmpare the distances between the triangle's vertices and the angles' measurements in the οriginal triangle and the image tο see if the side lengths and angles are preserved.

The distance between pοints A and B is 8, but the distance between  A'' and B'' is 4, as we can see. Similarly, the separatiοn between B and C is 6, whereas between B'' and C'' is 3. The dilatiοn dοes nοt preserve the triangle's side lengths as a result.

Nevertheless, it is clear that the angles between the sides were kept because the transfοrmatiοn invοlved bοth a reflectiοn and a dilatatiοn, bοth οf which prοtect angles.

Therefοre the cοrrect οptiοn is D. The dilatiοn preserves the side lengths and angles οf the triangle, while the reflectiοn dοes nοt preserve side lengths and angles.

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Answer:

x = 4\(\sqrt{3}\)

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

x² + 4² = 8²

x² + 16 = 64 ( subtract 16 from both sides )

x² = 48 ( take square root of both sides )

x = \(\sqrt{48}\) = \(\sqrt{16(3)}\) = \(\sqrt{16}\) × \(\sqrt{3}\) = 4\(\sqrt{3}\)

Step-by-step explanation:

To find the numerical limits for a D grade, we need to determine the cutoff points for the top 77% and bottom 8% of scores.

Using a standard normal distribution table or a calculator, we can find that the z-score cutoff points for the top 77% and bottom 8% are approximately 0.61 and -1.41, respectively.

To find the corresponding raw scores, we use the formula:

raw score = (z-score x standard deviation) + mean

For the top 77%, we have:

raw score = (0.61 x 7.2) + 81.6 = 86.392, which we can round up to 87

For the bottom 8%, we have:

raw score = (-1.41 x 7.2) + 81.6 = 70.848, which we can round down to 70

Therefore, the numerical limits for a D grade are scores below 87 and above 70.

Step-by-step explanation:

we need to use the standard normal distribution table for mean = 0, standard deviation = 1.

to use it for our normal distribution with mean = 81.6 and standard deviation = 7.2 we need to find the transformation from the standard normal distribution to our normal distribution.

this is done by the z-scores of the interval limits (the z-score tells us how many standard deviations the desired value is away from the mean value).

and to correlate the given %-values to the distribution interval limits, we need to look up the corresponding p-value (probability value) in the table.

and then we need to calculate backwards to get our specific interval limits.

for the D-grade we are looking for the upper limit to "below the top 77%", which is "below the bottom 23%".

we have to assume this means "below or equal to the bottom 23%", just in case.

the lower level will be "above the bottom 8%".

so, the p-value for 23% = 0.2300.

that gives us the z-score ≈ -0.74.

z-score = (interval-limit - mean-value)/standard-deviation

-0.74 = (interval-limit - 81.6)/7.2

-0.74×7.2 = interval-limit - 81.6

-5.328 = interval-limit - 81.6

interval-limit = 76.272 ≈ 76

the p-value for 8% = 0.0800.

that gives us the z-score ≈ -1.41

-1.41 = (interval-limit - 81.6)/7.2

-1.41×7.2 = interval-limit - 81.6

-10.152 = interval-limit - 81.6

interval-limit = 71.448 ≈ 71

the students with a score s

71 < s <= 76

get a D.

(greater than 71 but lower or equal to 76).