Kara mixes different colors of paint to create new colors. The table shows the amount of paint Kara mixes per batch.
Select all the batches that will create the same colors as the first batch.
A. Batch 2
B. Batch 3
C. Batch 4
D. Batch 5
E. Batch 6

Answer:

13.979

Step-by-step explanation:

log 625^5   =  5  log 625  = 5*2.79588=

Answer:

Exact Form:

1/4

Decimal Form:

0.25

Step-by-step explanation:

Answer:

128 because formula is bh

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

[tex] \frac{sin(56)}{78.6} = \frac{sin(90)}{ab} \\ \\ absin(56) = sin(90) \times 78.6 \\ \\ ab = \frac{sin(90) \times 78.6}{sin(56)} \\ ab = 94.8 \\ \\ {x}^{2} + {78.6}^{2} = {94.8}^{2} \\ {x}^{2} = {94.8}^{2} - {78.6}^{2} \\ {x}^{2} = 8987.04 - 6177.96 \\ {x}^{2} = 2809.08 \\ x = \sqrt{2809.08} \\ x = 53[/tex]

The probability that Natalie got at least two correct on the last three

true-or-false questions is 1/4.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The sample space is 2. The question is either correct or wrong.  

The probability that Natalie got at least two correct = 1/2 x 1/2 = 1/4

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Answer:

(x² -1) + y² = 9

Step-by-step explanation:

diameter=6 so radius means 6/2=3 (thus,radius²=3²=9)

centre (1 and midpoint of diameter is at y=0, so 1,0)

Answers are in bold

S1 = 1

S2 = 0.5

S3 = 0.6667

S4 = 0.625

S5 = 0.6333

=========================================================

Explanation:

Let [tex]f(n) = \frac{(-1)^{n+1}}{n!}[/tex]

The summation given to us represents the following

[tex]\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=\sum_{n=1}^{\infty} f(n)\\\\\\\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=f(1) + f(2)+f(3)+\ldots\\\\[/tex]

There are infinitely many terms to be added.

-------------------

The partial sums only care about adding a finite amount of terms.

The partial sum [tex]S_1[/tex] is the sum of the first term and nothing else. Technically it's not really a sum because it doesn't have any other thing to add to. So we simply say [tex]S_1 = f(1) = 1[/tex]

I'm skipping the steps to compute f(1) since you already have done so.

-------------------

The second partial sum is when things get a bit more interesting.

We add the first two terms.

[tex]S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\[/tex]

The scratch work for computing f(2) is shown in the diagram below.

-------------------

We do the same type of steps for the third partial sum.

[tex]S_3 = f(1)+f(2)+f(3)\\\\S_3 = 1+(-\frac{1}{2})+\frac{1}{6}\\\\S_3 = \frac{2}{3}\\\\S_3 \approx 0.6667\\\\\\[/tex]

The scratch work for computing f(3) is shown in the diagram below.

-------------------

Now add the first four terms to get the fourth partial sum.

[tex]S_4 = f(1)+f(2)+f(3)+f(4)\\\\S_4 = 1+(-\frac{1}{2})+\frac{1}{6}-\frac{1}{24}\\\\S_4 = \frac{5}{8}\\\\S_4 \approx 0.625\\\\\\[/tex]

As before, the scratch work for f(4) is shown below.

I'm sure you can notice by now, but the partial sums are recursive. Each new partial sum builds upon what is already added up so far.

This means something like [tex]S_3 = S_2 + f(3)[/tex] and [tex]S_4 = S_3 + f(4)[/tex]

In general, [tex]S_{n+1} = S_{n} + f(n+1)[/tex] so you don't have to add up all the first n terms. Simply add the last term to the previous partial sum.

-------------------

Let's use that recursive trick to find [tex]S_5[/tex]

[tex]S_5 = [f(1)+f(2)+f(3)+f(4)]+f(5)\\\\S_5 = S_4 + f(5)\\\\S_5 = \frac{5}{8} + \frac{1}{120}\\\\S_5 = \frac{19}{30}\\\\S_5 \approx 0.6333[/tex]

The scratch work for f(5) is shown below.

Answer:a=10 b=35

Step-by-step explanation:

1*8=8  1.25*8=10

1*28=28 1.25*28=35

Answer: 1)3.26.3

2)326.15

3)325.39

4)326.48

Step-by-step explanation: you want to start from the lowest number to get your answer

Answer:

84

Step-by-step explanation:

Answer:

[tex]\sf \theta=\dfrac34 \ radians=42.97 \textdegree \ (nearest \ hundredth)[/tex]

Step-by-step explanation:

Formulae

[tex]\sf radius (r)=\dfrac12 d[/tex]

(where d is the diameter of a circle)

[tex]\sf arc \ length =r\theta[/tex]

(where r is the radius and [tex]\theta[/tex] is measured in radians)

Calculation

Given:

Substituting these values into the formula for arc length:

[tex]\implies \sf 3 =4\theta[/tex]

[tex]\implies \sf \theta=\dfrac34 \ radians[/tex]

To convert radians to degrees use

[tex]\sf 1 \ rad \cdot \dfrac{180\texrdegree}{\pi}[/tex]

[tex]\implies \sf \dfrac34 \cdot \dfrac{180\texrdegree}{\pi}=42.97183463...\textdegree[/tex]

Now

[tex]\\ \rm\rightarrowtail \theta=\dfrac{l}{r}[/tex]

[tex]\\ \rm\rightarrowtail l=r\theta[/tex]

[tex]\\ \rm\rightarrowtail 3=4\theta[/tex]

[tex]\\ \rm\rightarrowtail \theta=\dfrac{3}{4}^c[/tex]

Answer:

=(-1,-5)

Step-by-step explanation:

y=X1=4

y=-2x-5-2

Answer:

301 feet

Step-by-step explanation:

plug in the known values

[tex]85=\sqrt{24d}[/tex]

square both sides to cancel the square root

[tex]7225=24d[/tex]

divide both sides by 24 to get d on its own

[tex]d=301.041[/tex] feet

to the nearest foot is 301 feet

Step-by-step explanation:

it just means

z = k×x²/y³

12 = k×8²/2³ = k×64/8 = k×8

k = 12/8 = 3/2

24 = k×x²/1³ = 3/2 × x²/1 = 3/2 × x²

24/(3/2) = x²

48/3 = x²

16 = x²

x = 4 or

x = -4

Answer:

4x+4=16

4x= 16–4

4x= 12

x= 12/4

x= 3

Alternatively,

4x+4=16

Taking 4 common,

4 (x+1) = 16

x+1 = 16/4

x+1 = 4

x = 4–1

x = 3

Step-by-step explanation:

The value of x is 68.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Parts of an Equation

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.

Given equation:

4/(x - 4) = 1 /16

Now, solving for x

4/(x - 4) = 1 /16

64 = x - 4

x= 68

Hence, the value of x is 68.

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Answer:

5 years ago

Step-by-step explanation:

5 years ago, they were 35 years old and 3 years old. 35*3=105.

Answer:

W = 5

L = 15

Step-by-step explanation:

Formula for Area of Rectangle is L × W

Since stated triple;

L = 3W

Area = L×W = 3W² = 75

It'll be:

3W² = 75

Divide both sides with 3:

3W² = 75

3 3

W² = 25

Then square root both sides:

w = 5

Again stated that length is triple the width:

L = 5 × 3

L = 15

Therefore;

W = 5

L = 15

Answer:

Step-by-step explanation:

If this is a parallelogram., this means that the opposite angles are congruent. Thus, the erasure of angle E is equal to the measure of angle G.

So, 10x-21=4x+27, meaning x=8.

Therefore, the measure of angle E is 10(8)-21=59 degrees

Step-by-step explanation:

The number 1 is a common factor of C) all whole numbers

Answer:

C

Step-by-step explanation:

6 / 1 = 6. 5 / 1 = 5. every whole number is divisble by 1, even prime numbers.

Answer:

7.5% compounded continuously yields the greatest return after 9 years

Step-by-step explanation:

Compounded interest = P(1+r/n)^(nt), where P is the principle, r is the rate of interest, n is the number of times compounded annually, and t is the time of the investment.

7.6% compounded semiannually:

I = 11000(1+0.076/2)^(2*9) --> 11000(1.038)^18 ~ $21525.09

7.5% compounded continuously:

Since it is compounded continuously, we use the mathematical constant e.

I = 11000e = $29901.01

Answer:

Cartesian product

Step-by-step explanation:

The Cartesian product of two sets, X and Y, denoted by X × Y, is the set of all ordered pairs (x, y), where x is an element of X and y is an element of Y: 8 (2.4.1) X × Y = { (x, y) ∣ x ∈ X ∧ y ∈ Y } For example, if Children = { Peter, Mark, Mary }, and Parents = { Paul, Jane, Mark, Mary }, then

The missing numerator that will make the rational expressions equivalent is (82x + 7) / (12x + 42)

An equation is an expression that shows the relationship between two or more variables and numbers.

Let y represent the missing numerator, hence:

82x + 7 = y * 6(2x+7)

82x + 7 = y * (12x + 42)

y = (82x + 7) / (12x + 42)

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Answer:

the answer is D...... ..........

Answer:

226,080 cm3

Step-by-step explanation:

Answer:

Meterstick

Step-by-step explanation: A standard classroom is basically just a large open room, no rooms. So it is more straight than it is curved, and if you can cover a larger area in a shorter time, it is more effecient.

Answer:

a = -14

Step-by-step explanation:

f(a) = -43

3a - 1 = -43

3a    = -43 + 1

  3a  = -42

     a = -42/3

    a = -14

Using the normal distribution and the central limit theorem, we have that:

a) The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.

b) There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.

c) There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

The mean and the standard error are given by:

[tex]\mu = p = 0.22[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.22(0.78)}{150}} = 0.0338[/tex]

The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.

Item b:

The probability is one subtracted by the p-value of Z when X = 0.25, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.25 - 0.22}{0.0338}[/tex]

Z = 0.89

Z = 0.89 has a p-value of 0.8133.

1 - 0.8133 = 0.1867.

There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.

Item c:

The probability is the p-value of Z when X = 0.2 subtracted by the p-value of Z when X = 0.15, hence:

X = 0.2:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.2 - 0.22}{0.0338}[/tex]

Z = -0.59

Z = -0.59 has a p-value of 0.2776.

X = 0.15:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.15 - 0.22}{0.0338}[/tex]

Z = -2.07

Z = -2.07 has a p-value of 0.0192.

0.2776 - 0.0192 = 0.2584.

There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.

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Answer:

16641

Step-by-step explanation:

Thank you!