Tell whether the ratios form a proportion. 14:8 and 28:10

Answer:

4 inches

Step-by-step explanation:

Jerry built a 2 inch cube to hold his marble collection.

Volume of this cube = 2³ = 8 cubic inches

He wants to build a cube with a volume 8 times larger.

Hence: 8 × 8 in³ = 64 in³

The measurement of each edge is calculated as:

√64 in³ = 4 inches

The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity is equal to the number of total observations (N) minus the number of groups (k). So, it can be represented as (N - k).

The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity depend on the sample size and the number of groups being compared.

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Based on the given task content, the identity property of each of the questions are below:

4 + (x + y) = (4 + x) + y

If √49 = 7 and 7 = 3 + 4, then √49 = 3 + 4

(mn) × 1 = mn

(x + 3) × 0 = 0

(x + 2) + y = (2 + x) + y

2(1/2) = 1

3 = 3

10k² + (-10k²) = 0

5(x + 7) = 5x + 35

If -7v = 28, then 28 = -7v

Distributive property states that multiplying the sum of two or more number gives the same result.

Transitive Property states that for all real numbers x ,y, and z, if x=y and y=z , then x=z.

The additive inverse property states that adding a number and the inverse of the same number gives a sum of 0.

The multiplicative inverse property states that multiplying a nonzero number with the inverse of the same nonzero gives a product of 1.

The reflexive property of equality states that a number is always equal to itself, that 1 = 1

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The mean number of peas with green pods in groups of 38 is 9.5 peas, and standard deviation is 2.671 peas.

To find the mean and standard deviation, we will use properties of a binomial distribution. In this case, the probability of a pea having green pods is 0.25 and we are randomly selecting groups of 38 peas.

The mean (μ) of a binomial distribution is given by the formula μ = n * p,. The n = 38 and p = 0.25.

The mean is μ:

= 38 * 0.25

= 9.5 peas.

The standard deviation (σ) of a binomial distribution is given by the formula σ = \(\sqrt{(n * p * (1 - p)}\).

\(= \sqrt{38 * 0.25 * (1 - 0.25}\\= \sqrt{38 * 0.25 * 0.75}\\= \sqrt{7.125}\\= 2.671.\)

Full question:

Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.25 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 38. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 38 The value of the mean is 9.5 peas.

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Answer:

D. 300

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Variables

Stuffed bears = b

Stuffed dogs = d

Step 2: Define Systems

$7b + $8d = $3800

b + d = 500

Step 3: Rewrite Systems

b + d = 500

Step 4: Redefine Systems

7b + 8d = 3800

-7b - 7d = -3500

Step 5: Solve for d

Elimination

Step 6: Define Answer

d = 300 means that the students bought 300 stuffed dogs.

Answer:

D

Step-by-step explanation:

Remark

Let the stuffed bear = x

Let the stuffed dog = y

Equations

x + y = 500                   (1)

7x + 8y = 3800               (2)

Solution

There are two ways you could do this. You can use substitution or you could use multiplying equation 1 by either 7 or 8 to get rid of the x or y.

Multiply (1) by 7

7x + 7y = 3500             (3)       Write equation (2) below (3) and subtract

7x + 8y = 3800                        Subtract

    -y = - 300                            Multiply by - 1

     y = 300

Use the result for y to get x using equation 1

x + y = 500

x + 300 = 500                         Subtract 300

x = 500 - 300

x = 200

Stuffed bears = 200

Stuffed dogs   = 300

The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Answer: 4 days

Step-by-step explanation:

If it takes 4 people 8 days to paint a wall. We can only assume that doubling the number of people would be 2 times as fast. So divide 8/2=4.

The missing values are:

BC = 25, BN = 16, NC = 9, and AN = 12

Given:

AB = 20

AC = 15

Using the Pythagorean theorem in triangle ABC:

CB = √AC² + AB²

CB= √20² + 15²

CB= √625

CB= 25

Since, AN is altitude we have ΔNBA~ΔABC and ΔNAC~ΔABC

BN / AN = BA / CB

BN/ 20= 20/25

BN = 16

and, AN / BA = AC / CB

AN /20 = 15/ 25

AN = 12

Now, CN=  CB - BN

CN = 25- 16

CN= 9

BC^2 = 20^2 + 15^2

BC^2 = 400 + 225

Since ΔANC is a right triangle so

AN = √15²-12²

AN = √81

AN = 9

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Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

The answer is 2.00.

Step-by-step explanation:

45.15 ÷ 21 = 2.15

2.15 rounded off to the nearest whole number is 2.00.

This was because you asked for an estimate.^

Answer: y=31-5x

Step-by-step explanation:

subtract the 5x to the other side to get y.

The value P(t), in dollars, of the bank account is growing according to the equation. The future value of the account at time t=6 is approximately $2,118.96. This is a first-order linear differential equation of the form

DP/dt - 0.05 P = 15 ,I(t) = e(int(-0.05dt)) = e(-0.05t)

Multiplying both sides of the equation by the integral factor gives:

e(-0.05t)DP/dt - 0.05e(-0.05t)P = 15e(-0.05t)

Using the product rule, the left-hand side can be written as

d/dt(e(-0.05t) P) = 15e(-0.05t)

e(-0.05t) P = -300e(-0.05t) + C

where C is the constant of integration. You can solve C using the initial condition P(0) = $1,300.

e0 * 1300 = -300e0 + C

C=1600

e(-0.05t) P = -300e(-0.05t) + 1600

P(t) = -300 + 1600e(0.05t) .To find the future value of the account at time t=6, substitute t=6 into the formula.

P(6) = -300 + 1600e(0.05*6)

P(6) ≒ $2,118.96

Thus, the future value of the account at time t=6 is approximately $2,118.96. 

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Complete question: The value P(t), in dollars, of the bank account is growing. According to the equation DP/dt - 0. 05P = 15,  If an initial amount of P(0) = $1,300 is deposited to the account, then the future value of this account at time t = 6 is approximately?

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Answer:

(3,6)

Step-by-step explanation:

From 6 in the x-axis go up 3 units, and from 3 on the y-axis go left 6 units.

Answer:

Divide the figure above into a cylinder and a dome

+) the volume of the dome is

\(v1 = \frac{1}{12} \pi6 {}^{3} = 18\pi\)

the surface area is

\(s1 = \pi3 {}^{2} = 9\pi\)

+) the volume of the cylinder is

\(v2 = \pi.3 {}^{2} .13 = 117\pi\)

the surface area is

\(s2 = 2\pi.3.13 + 2\pi.3 {}^{2} = 96\pi\)

so the volume of this figure is

\(v = v1 + v2 = 18\pi + 117\pi = 135\pi\)

the surface area of this figure is

\(s = 9\pi + 96\pi = 105\pi\)

The number of ways to order the first, second and third place finishers is simply the number of permutations of 8 runners taken 3 at a time. This can be calculated using the formula for permutations

The formula for permutations, P(n,r), gives the number of ways to choose r items from a set of n items, where order matters. This formula is calculated as:

P(n,r) = n! / (n-r)!

where n! represents the factorial of n (i.e. n multiplied by n-1 multiplied by n-2, etc. down to 1).

In this problem, n = 8 and r = 3, so the number of permutations is:

P(8,3) = 8! / (8-3)! = 8! / 5! = 40320 / 120 = 336

So there are 336 different arrangements of first, second, and third place finishers in the 100-meter sprint.

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The correct simplification of the expression is c12 (option c).

The expression (c^4)^3 can be simplified using the exponent rules for powers of a power, which states that when a power is raised to another power, we can multiply the exponents.

Thus, we have:

(c^4)^3 = c^(43) [Using the rule (a^m)^n = a^(mn)]

Simplifying the exponent 4*3, we get:

c^(4*3) = c^12

Therefore, the correct simplification of the expression is c^12.

Option (c) is the correct answer as it correctly represents the simplified form of the given expression. Option (a) c^-1, option (b) c^7, and option (d) c^64 are not correct because they do not follow the exponent rules used to simplify the expression.

In summary, the expression (c^4)^3 simplifies to c^12, which is option (c) in the given options.

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The factory overhead efficiency variance for May is $480 unfavorable.

What is overhead efficiency variance ?

The overhead efficiency variance measures the difference between the actual hours worked and the standard hours allowed, multiplied by the standard overhead rate.

Step 1: Budgeted overhead at 90% capacity:

Budgeted overhead = 6,120 DLHs * $3.00 per DLH = $18,360

Step 2: Budgeted overhead at 70% capacity:

Budgeted overhead = $15,640

Step 3: Standard hours at 70% capacity:

Standard hours = 6,120 DLHs / 90% * 70% = 4,760 DLHs

Step 4: Variable overhead rate:

Variable overhead rate = ($18,360 - $15,640) / (6,120 DLHs - 4,760 DLHs) = $2.00 per DLH

Step 5: Variable overhead efficiency variance:

Variable overhead efficiency variance = (4,760 DLHs - 5,000 DLHs) * $2.00 = $480 unfavorable

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The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The total amount of sugar which contains in 4 grams of sugar = 304 grams.

Amount of sugar fast food smoothie has = 76 gram

amount of sugar a teaspoon of sugar contains = 4 gram

Thus the total amount of sugar which contains in 4 grams of sugar = 4 × 76

this implies  the total amount of sugar which contains in 4 grams of sugar  = 304 grams

In this question we used the unitary method where we multiplied a quantity with a known quantity to find the value of an unknown quantity.

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Before we solve the equation let's take a look at it.

f(x) = -2x + 3

See how x appears in both f(x) and as the variable in the second half of the equation?

f(x) means "The function of x." You might also see g(x), h(x), and while those are the most common it can really be any letter, and any variable inside the parentheses.

So when we see f(-1), that means "The function of -1" or "The function of x when it is equal to -1."

Catching on? We need to replace x with -1 to solve for f(-1).

So here we go:

f(x) = -2x + 3

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

f(-1) = 2 + 3

f(-1) = 5

Voilà! We have solved for f(-1). Hope this helped.

Answer:

A.

Step-by-step explanation:

Answer:

Step-by-step explanation:

see attached image.

perimeter of trapezoid = sides (6 + 8 + 5 + 8 + 8)

                                     = 35

the perimeter of trapezoid BMNC is 35

Given :

In  triangle ABC shown below, L is the midpoint of BC, M is the midpoint of AB, and N is the midpoint of AC. If MN = 8, ML = 5, and NL = 6

By midpoint theorem ,

\(BC= 2 \cdot MN\\BC=2 \cdot 8\\BC=16\)

M is the midpoint of AB, AB= 2 times NL

BM=NL

BM=6

N is the midpoint of AC

AC is 2 times of ML

NC=ML

NC=5

Perimeter of trapezoid is  sum of all the sides

Perimeter of BMNC = BM+MN+NC+CB

Perimeter =\(6+8+5+16=35\)

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Answer:

7.9

Step-by-step explanation:

area of circle equals π× 5 = 15.7

area of half of the circle equals 15.7÷2

=7.85

now round it of and it's 7.9

Answer:

1. -1/2

2. Graph attached below:

Step-by-step explanation:

1) To find to slope of the line with two points would be the following equation:

\(y_{2} - y_{1} / x_{2} - x_{1}\)

So let’s assume our variables and subsitute them to see that the Carma’s Working out is an error.

Form: \((x_{2}, y_{2}), (x_{1}, y_{1})\)

\(y_{2} = 3\)

\(y_{1} = 1\)

\(x_{2} = 7\)

\(x_{1} = 11\)

\(3 - 1 / 7 - 11 = -1/2\)

1. Error one: The point values of the slope aren‘t correctly labeled and are not the same form as in the formula.

2. Error two: The slope output is not correct, it is 2 but the slope is -1/2.

Now let’s get on the graph of Carma’s workout, I can spot that the point (-4, 5) is not plotted correctly. Instead it is plotted (4, -5). To understand clearly I will label these points on a graph, image attached below:

3. Error three: The point (-4, 5) is not plotted correctly, x should be negative and y should be positive.

4. Error four: The slope is not correct, instead the slope of the graph is negative but we need a positive slope.

Now it is time to fix Carma’s mistakes:

1) Slope: -1/2

2) Graph attached below

The wavelength of the baseball is approximately 1.277 x 10^-35 meters.

To calculate the wavelength of the baseball, we can use the de Broglie wavelength equation, which relates the wavelength (λ) to the mass (m) and velocity (v) of an object. The equation is given by:

λ = h / (m * v)

where λ is the wavelength, h is the Planck's constant (h = 6.626 x 10^-34 J·s), m is the mass of the baseball (155 g = 0.155 kg), and v is the velocity of the baseball (32.5 m/s).

Substituting the given values into the equation, we have:

λ = (6.626 x 10^-34 J·s) / (0.155 kg * 32.5 m/s)

To simplify the calculation, we can first convert the mass to kilograms:

λ = (6.626 x 10^-34 J·s) / (0.155 kg * 32.5 m/s)

Now, we can multiply the numerator and denominator by 1000 to convert the mass to kilograms:

λ = (6.626 x 10^-34 J·s) / (0.155 kg * 32.5 m/s)

λ = (6.626 x 10^-34 J·s) / (0.155 kg * 32.5 m/s)

Calculating the numerator and denominator separately, we get:

λ ≈ 1.277 x 10^-35 m

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