Patricia bought 4 apples and 9 bananas for $12. 70 Jose bought 8 apples and I bananas for $17. 70 at the same grocery store What is the cost of one apple?​

Answer:

Step-by-step explanation:

Write out the first 4 terms of an infinite geometric series whose sum, S = 2/(4 - 6x ^ 4)

Answer:

2x+6

Step-by-step explanation:

To simplify an expression such as this you must add like terms. Like terms are terms that have the same variable and power. In this expression 4x, x, -3x are like terms and -2 and 8 are also like terms. To add like terms simply add the coefficients and remember adding a negative is the same as subtracting. So, add the previously listed terms 4x + x + (-3x) = 2x, then -2+8= 6. This means the simplified expression is 2x+6.

Answer:

39

Step-by-step explanation:

quarters are worth $.25. just divide 9.75 by .25 and you get your answer.

9.75 ÷ .25 = 39

Answer:

39

Step-by-step explanation:

39 x 25 = 975

Answer:

2.67 minutes or 2 2/3 minutes

Step-by-step explanation:

To find the amount of time she spent on each you would divide the time by amount

16 / 6 = 2.6666...

Rounded = 2.7 minutes

The binomial test is used to test the hypothesis HH0: p = p0 in a binomial distribution.

In the binomial test, we calculate the probability of observing the given data or more extreme data, assuming that the null hypothesis is true. If this probability, known as the p-value, is small (usually less than 0.05), we reject the null hypothesis in favor of the alternative hypothesis.

To perform the binomial test, we can follow these steps:

1. Define the null hypothesis HH0: p = p0 and the alternative hypothesis HA: p ≠ p0 or HA: p > p0 or HA: p < p0, depending on the research question.

2. Calculate the test statistic using the formula:
  test statistic = (observed number of successes - expected number of successes) / sqrt(n * p0 * (1 - p0))

3. Determine the critical value or p-value based on the type of test (two-tailed, one-tailed greater, one-tailed less) and the significance level chosen.

4. Compare the test statistic to the critical value or p-value. If the test statistic falls in the rejection region (critical value is exceeded or p-value is less than the chosen significance level), reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Remember, the binomial test assumes independence of the binomial trials and a fixed number of trials.

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Step-by-step explanation:

Substitute the given values into the expression;

\(12(3) - 3( \frac{1}{3} ) \div 4(3) - 5\)

Multiply;

\(36 - 1 \div 12 - 5\)

Solve Using PEMDAS;

\(36 - \frac{1}{12} - 5\)

\(35 \frac{11}{12} - 5\)

\(\boxed{30 \frac{11}{12} } \)

The orthogonal matrix S is

S = [1/√3 1/√3]

     [1/√3 -1/√3]

     [1/√3 1/√3]

To find an orthogonal matrix S such that S^(-1)AS is a diagonal matrix D, we need to find the eigenvectors of matrix A.

Given matrix A:

[0 2]

[2 0]

To find the eigenvectors, we solve the characteristic equation:

|A - λI| = 0

where λ is the eigenvalue and I is the identity matrix.

(A - λI) =

[0 - λ 2]

[2 0 - λ]

Expanding the determinant:

(-λ)(-λ) - 2(2) = λ^2 - 4 = 0

Solving for λ:

λ^2 = 4

λ = ±2

For λ = 2:

(A - 2I)v = 0

[0 - 2 2] [v1] = [0]

[2 0 - 2] [v2] [0]

Simplifying the system of equations:

-2v2 + 2v3 = 0

2v1 - 2v3 = 0

Solving the equations, we find v1 = v2 = v3.

Therefore, one eigenvector corresponding to λ = 2 is [1 1 1].

For λ = -2:

(A + 2I)v = 0

[0 2 2] [v1] = [0]

[2 0 2] [v2] [0]

Simplifying the system of equations:

2v2 + 2v3 = 0

2v1 + 2v3 = 0

Solving the equations, we find v1 = -v2 = v3.

Therefore, another eigenvector corresponding to λ = -2 is [1 -1 1].

To find the orthogonal matrix S, we normalize the eigenvectors:

v1 = [1 1 1] / √3

v2 = [1 -1 1] / √3

Now, we can construct the matrix S using the eigenvectors as columns:

S = [v1 v2]

[--- ---]

[--- ---]

Substituting the normalized eigenvectors:

S = [1/√3 1/√3]

[1/√3 -1/√3]

[1/√3 1/√3]

Therefore, the orthogonal matrix S is:

S = [1/√3 1/√3]

[1/√3 -1/√3]

[1/√3 1/√3]

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Answer:

Step-by-step explanation:

(f + g)(x) = 2x + 8 + 55

             = 2x + 63

(f + g)(3) = 2*3 + 63

             = 6 + 63

             = 69

Answer:

19

Step-by-step explanation:

On ap.ex its g(x)=5 not 55

2x+8+5

2(3)+13---->19

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

Step-by-step explanation:

So you have a square that has a perimeter of 36.

A square has 4 equal sides.

z+z+z+z=36          or              4z=36

We are asked to determine the equation of a line with a slope 1/3. The general form of a line equation is:

Where "m" is the slope and "b" the y-intercept.

Now, we substitute the value of the slope:

Now, to determine the value of "b" we will use the fact that the line passes through the point (x, y) = (

6, 8). Now, we plug in these values in the equation:

Solving the product on the right side we get:

Now, we subtract 2 from both sides:

Now, we substitute the value in the equation of the line:

And thus we get the equation of the line.

Answer:

i wanna say 15 maybe, but it might be wrong. I havent done these type of problems in awhile.

We will thus require 62 cubοid bricks tο create the wall, tο the clοsest whοle brick.

A nοrmal brick is a cubοid, a three-dimensiοnal structure with six rectangular faces.

We need tο have at minimum 42/18 = 2.33 rοws mοre bricks because the wall is 42 inches tall, and each brick is 18 inches tall. We require three rοws οf bricks since we can't have a half rοw.

We require 144/7 = 20.57 bricks each rοw because the wall is 144 inches lοng and each brick is 7 inches lοng. There must be 21 bricks each rοw because we cannοt have half bricks.

The first rοw requires 21 whοle bricks. If a brick is sliced in half, the οther half can be used οn the οther end οf the identical rοw.

21 whοle bricks are alsο required fοr the secοnd rοw. Fοr the remainder οf the rοw, we need οnly 20 full bricks since we can utilise the half-brick we cut during the initial rοw just at start οf the secοnd rοw.

The third rοw requires 21 whοle bricks. We have a spare half-brick that we may utilize at the cοnclusiοn οf the third rοw since we utilized οne in the first rοw.

Hence, 62 cοmplete bricks are needed, which equals 21 + 20 + 21.

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Answer:

  2500.49

Step-by-step explanation:

  --Given--

    Amount (A): $3571.31

           Rate (r): 4%

Compound (n): 2                          **semi-annually means 2 times a year**

           Time (t): 9                          **2016 to 2025 is 9 years time**

  --Solve--

     P = A / (1 + r/n)^nt

         = 3571.31 / (1 + .04/2)^(2 * 9)

         = 3571.31 / (1.02 )^(18)

         = 3571.31 / 1.02¹⁸

         = 3571.31 / 1.02¹⁸

         = 3571.31 / 1.428246

         = 2500.49

Answer:

Volume of the counter = Length × Width × Height

                                      = 19 1/2 × 8 3/4 × 2

                                      = 341 1/4 cubic metres

Answer:

There is only one solution set.

Step-by-step explanation:

The set can contain any number of solutions or none.

This is all I know, hope it helps.

The radius of this circle to the nearest tenth is equal to 1.3 units.

In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.

Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = rθ

Where:

By substituting the given parameters into the arc length formula, we have the following;

12.8 = r × 9.8

Radius, r = 12.8/9.8

Radius, r = 1.3 units.

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Answer:

Step-by-step explanation:

Here you go mate

Step 1

3+(-4)-8-(-1)  Equation/Question

Step 2

3+(-4)-8-(-1) Simplify

-9-(-1)

Step 3

-9-(-1)  Subtract them

-9-1

Answer

-8

Hope this helps

Answer:

Because √25 = 5 and 5 can be written in the form of a fraction 5/1.

Step-by-step explanation:

It proves that √25 is rational.

Answer:

the square toot of 25 is = 5

Step-by-step explanation:

therefore

5√5

= 25

√25 is equal to 5

= 5

i hope it helps

Answer:

60.01778

Step-by-step explanation:

Answer:

The mean is 3

Step-by-step explanation:

Answer:

Rate( family drink juice) = 0.1142 gallon juice per day

Step-by-step explanation:

Given:

Amount of juice drank by family = 4 gallon

Time taken by family = 5 week

Find:

Rate( family drink juice)

Computation:

Time taken by family (In days) = 5 x 7 days

Time taken by family (In days) = 35 days

Rate( family drink juice) = Amount of juice drank by family / Time taken by family (In days)

Rate( family drink juice) = 4 / 35

Rate( family drink juice) = 0.1142 gallon juice per day

Answer:

-62

Step-by-step explanation:

180-w+49(angles  on  a straight line=180)

angles on a triangle=180

Hence,

         180-w+49+w+17+w-4=180

collect the like terms

180+49+17-4+w+w-w=180

242+w=180

Take 180 to the other side and also w

242-180=-w

62=-w    same as w=-62

Answer:

70 degrees

Step-by-step explanation:

To find the value of J, both of the smaller angles need to be added together

40 + 30 = 70

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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Answer:

Step-by-step explanation:

The 2 smaller triangles are proportionate to one another because they are 2 parts of the same larger triangle. Setting up the proportion, one triangle at a time:

\(\frac{x}{8.3} =\frac{11.6}{6.7}\) and cross multiply to get

6.7x = 96.28 so

x = 14.37 or 14.4, choice A.

Answer:

angle 4 and angle 8

angle 3 and angle 5

Step-by-step explanation: the pair of angles on one side of the transversal and inside the two lines are called the consecutive interior angles  

so, angle 4 and angle 8

and angle 3 and angle 5

are consecutive interior angles.

Aaron's taxable income is negative (-$10,100), it means that he does not have any taxable income.

To determine the amount of taxable income for Aaron Rentz in 2020, we need to consider his wages, interest income, and any deductions or credits he may be eligible for.

From the given information, Aaron has $900 of wages and $1,400 of interest income.

In 2020, the standard deduction for a single individual was $12,400. Since Aaron is a qualifying child of his parents, he may not be able to claim his own personal exemption.

To calculate Aaron's taxable income, we subtract the standard deduction from his total income:

Taxable Income = Total Income - Standard Deduction

Taxable Income = $900 + $1,400 - $12,400

Taxable Income = $2,300 - $12,400

Taxable Income = -$10,100

Since Aaron's taxable income is negative (-$10,100), it means that he does not have any taxable income.

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