Marta buys x candles and y books at a store.
• Each candle costs $6, and each book costs $14.
• She spends no more than $65.
• She buys more than 8 items total.
Create two inequalities using x and y to model the situation.

A. Poor understanding of HIV

B. Cognitive impairment

C. Substance abuse

D. Unstable housing

Answer:

Step-by-step explanation:

1st angle = (2x+6)° = (56 + 6)°= 62°. 2nd angle = x = 28°. Thus, 62° and 28° are the required angles. Answer.

An auditor selects a sample of shipping documents to examine whether invoices were created for this sample. The fundamental objective of the audit, Completeness, will be satisfied by this test.

Given,

An auditor picks a sample of shipping papers to examine if the related sales invoices were produced.

We need to determine what kind of audit aim will be the focus of this test's evidence gathering;

Audit purpose;

An audit's objective is to form an unbiased evaluation of the entity's financial statements. It is a component of the opinion if the financial statements give a true and fair picture and have been accurately prepared in accordance with accounting rules.

Here,

The audit objective completion test was carried out by the auditor to acquire proof.

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The question is incomplete. Completed question is given below;

An auditor selects a sample of shipping documents in order to determine if the related sales invoices were prepared. This test would gather evidence concerning which audit objective?

A) Completeness

B) Detail tie-in

C) Occurrence

D) Realizable value

The variance for the data set is 18.

What is a variance?

The term variance refers to a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set.

Here we have to find the variance for this data set.

Given data:

The age of six grandchildren in a family is = 6, 3, 14, 11, 14, 6

The mean = 6+3+14+11+14+6/ 6

                 = 9

The variance = (6-9)² + (3-9)² + (14-9)² +(11-9)² + (14-9)² + (6-9)²/ 6

                      = 9+36+25+4+25+9/  9

                     = 18

Therefore the variance is 18.

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As a fraction of c, the length will be 60% at v/c = 0.76

The length of the moving rod = 60%

Using the formula for length contraction-

L = L_o(√(1 - (v²/c²))

Where;

v = The speed of the object

c = The speed of light

L = The length of the object at a moving speed

L_o = The length of the object at rest

Thus,

L = 65%

L_o = 0.65

Substituting the values -

0.65L_o = L_o[√(1 - (v²/c²))]

Dividing both sides by L_o -

0.65 = √(1 - (v²/c²))

Squaring both sides -

0.65² = (1 - (v²/c²))

v²/c² = 1 - 0.65²

v²/c² = 0.5775

Taking the square root of both sides gives;

v/c = 0.76

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Answer:

6 hours

Step-by-step explanation:

dg's plumbing and heating charges $50 plus $60 per hour for emergency service. bill remembers being billed just over $400 for an emergency call. how long to the nearest hour was the plumber at bill's house?

60h + 50 > 400

subtract 50 from both sides:

60h > 350

divide both sides by 60:

h > 5.8333

rounded: 6 hours

Answer:

64

Step-by-step explanation:

16 ÷ 12 = 1.33 (rounded to 2 decimal places)

1.33 = scale factor

1.33² = area scale factor

1.33² × 36 = 64 (rounded to a whole number)

Answer: 64 would be the area

Step-by-step explanation:

Answer:

Step-by-step explanation:

its 20

(a) 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.

(b) at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.

Given that,

A ship sets out from port at noon with a bearing of s 23° west and a speed of 10 knots.

We have to find

(a) By the time it gets dark at six o'clock, how far south and west will the ship have sailed? The ship alters its course to head due west at 6:00 p.m. miles south miles west

(b). at 7:00 p.m., determine the ship's bearing and distance from the port. nautical miles in s.

We know that,

(a) For 6:00 p.m

Sin(θ)=opposite/ hypothesis

θ=29

Opposite=west

Hypothesis =60

Sin(29°)=w/60

w=29.09nm

West= 29.09nm

Cos(θ)=adjacent/ hypothesis

θ=29

Adjacent= south

Hypothesis =60

Cos(29°)= south/60

south=52.475nm

Therefore, 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.

(b) tan(θ)=opposite/adjacent

Opposite=29.09nm

Adjacent= 52.475nm

Tan(θ)=29.09nm/52.475nm

θ=36.68°

Therefore, at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.

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We can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

What is the null hypothesis?

The null hypothesis is a common statistical theory that asserts that no statistical relationship or significance exists between two sets of observed data and measured phenomena based on a single observed variable.

Hypothesis:

[tex]H_0:\rho_1=0\\H_1:\rho\neq0[/tex]

Test statistic:

[tex]t=r\times\sqrt{\frac{n-2}{1-r^2} }\\\\ t=(0.8691)\times\sqrt{\frac{30-2}{(1-0.8691)^2} } \\\\t=9.2974[/tex]

D.F. = n - 2 = 28

P-value = P-value at t = 9.2974, ∝=0.05, 28 d.f. is

        P-value = 0.000

Conclusion: Since. P-value < ∝=0.05, so we have to reject the null hypothesis.

Hence, we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

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Answer:

Yes

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

for 2 days it's 98

then 300-90=202

202÷0.40=505

Answer:

b. 1 1/4

c. 11 3/8

d. 1 4/7

Step-by-step explanation:

b. 3 - 1 3/4

   2 4/4 - 1 3/4

   [4/4 - 3/4 = 1/4] and [2 - 1 = 1]

   1 + 1/4

   1 1/4

c. 7 3/8 + 4

   Add the whole numbers.

   11 3/8

d. 4 - 2 3/7

   3 7/7 - 2 3/7

   [7/7 - 3/7 = 4/7 and 3 - 2 = 1]

   1 + 4/7

   1 4/7

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Answer:

The goal is to make the denominators the same.

[tex]\frac{numerator}{denominator}[/tex]

Here's how to solve "b" (I explained it so you can do the other ones)

b.

[tex]3 - 1\frac{3}{4}[/tex]

Turn the 3 into a fraction (you can put any number over 1 and it will be the same)

[tex]\frac{3}{1} - 1\frac{3}{4}[/tex]

Next, let's turn the [tex]1\frac{3}{4}[/tex] into an "improper fraction". Right now, it is a mixed number. Multiply the denominator by the whole number on the left, and then add it to the numerator. The denominator will stay the same.

4 * 1 = 4

4 + 3 = 7

[tex]1\frac{3}{4}[/tex] → [tex]\frac{7}{4}[/tex]

Okay, so now we have this:

[tex]\frac{3}{1} - \frac{7}{4}[/tex]

This is getting easier! But to subtract, we have to make the denominators the same. Let's multiply the top and bottom of [tex]\frac{3}{1}[/tex] by 4.

[tex]\frac{3 * 4}{1 * 4} = \frac{12}{4}[/tex]

Now we have:

[tex]\frac{12}{4} -\frac{7}{4}[/tex]

One final step, subtract the numerators! Leave the denominators as they are.

12 - 7 = 5

Our answer is:

[tex]\frac{5}{4}[/tex]

The value of the the function h(x) at x = 4 is given as follows:

8.7.

The quadratic regression equations for each table are given as follows:

The function for the first item is defined as follows:

h(x) = 50/(5.5 + 8e^(-0.9x)).

At x = 4, the value assumed by the function is obtained replacing the lone instance of x by 4, hence:

h(4) = 50/(5.5 + 8e^(-0.9(4))).

Then a calculator is used to obtain the exact value due to the exponential, hence:

h(4) = 8.7.

The regression equations are obtained inserting the points of each table into a quadratic regression calculator.

For the first table, the points are given as follows:

(16, 15), (18, 15.6), (20, 15.7), (21, 15), (23, 13.1), (26, 8.9), (27, 6.6).

Hence the equation is of:

y = -0.127x² + 4.699x - 27.777.

For the second table, the points are given as follows:

(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).

Hence the equation is of:

y = 32.86x² - 379.14x + 1229.14.

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The statement of the given hypothesis condition is False.

What is hypothesis testing?

A type of statistical inference known as hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution.

Given this, A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys.

i.e. [tex]\mu_{1} > \mu_{2}[/tex]

">" sign implies that right-tailed test i.e. one-tailed right-sided.

Hence, the given statement is FALSE.

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Answer:

1. The GCF is 15 and the LCF is 1.

There are 4 common factors: 1, 3, 5, 15

2. The GCF and LCF is 1. This is the only common factor.

Step-by-step explanation:

To find common factors, think about what two numbers you can multiply to get the desired values. The numbers that are the same for both desired values are going to be factors.

The result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] is (x+2)/( 4x+3).

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

Given the following function:

[tex]f(x)=x^2-8x+4;\;g(x)=4x+3;\;and\;h(x)=x+2.[/tex]

We need to find the result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex]

Therefore,

g(x)=4x+3

h(x)=x+2

[tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] =(x+2)/( 4x+3)

Hence, the result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] is (x+2)/( 4x+3).

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Answer: The relationship between points R , S , and T is that the sum of the RS and RT will be equal to  RT that is RT=RS+ST

Step-by-step explanation:

The probability that [tex]\bar{x}[/tex] < 1.57 for the given mean, standard deviation , and samples is equal to 0.0162.

As given in the question,

Normal distribution with mean 'μ' = 1.59 millimeters

Standard deviation 'σ' = 0.042 millimeters

Sample size 'n' = 20

standard error = σ /√n

                        = 0.042 / √20

                        = 0.00933

Probability that [tex]\bar{x}[/tex] < 1.57  is

X = 1.57

s = 0.0093

P( X < 1.57)

= P[ (X -μ)/s < ( 1.57 - 1.59)/ 0.0093]

= P ( z < -2.14 )

Using z - table p value is

= 0.01617

= 0.0162

Therefore, the probability for the [tex]\bar{x}[/tex] < 1.57  is equal to 0.0162.

The complete question is :

A factory makes components used in jet engines, including reinforced steel washers. the washers are required to have a very precise thickness. the thickness of the washers follow a normal distribution with mean 1.59 millimeters and standard deviation 0.042 millimeters. a technician randomly samples n = 20 washers and calculates the mean of their thicknesses, which is x¯. what is the probability that x¯<1.57?

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The area of rectangular region r is = 12.

Given:

each diagonal of r has length 5. the perimeter of r is 14.

Let l and b be the length and breadth of a rectangle.

we know that

perimeter of rectangle = 2 ( l + b )

2 ( l + b ) = 14

divide by 2 on both sides

( l + b ) = 14/2

l + b = 7

l = 7 - b

l^2 + b^2 = d^2

( 7 - b )^2 + b^2 = 5^2

7^2 + b^2 - 2 * 7 * b  + b^2 = 25

49 + 2b^2 - 14b = 25

2b^2 - 14b + 24 = 0

on solving b = 4,3

Take any one value

b = 4

l = 7 - 4

l = 3

Area of rectangle = l * b

= 4 * 3

= 12

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Answer: 75%

Step-by-step explanation:

9 + 3 = 12

9/12 = 3/4

3/4 = 75%

If the wheel rotates clockwise, the height function is h(t) = 28.5 + 22.5sin(270 - 36t).

The function's central axis for the height of the Ferris wheel's center is given by h = f(t).

= 6 + 45 ÷ 2 = 6 + 22.5 = 28.5 meters.

The wheel rotates at a speed of 36 degrees per minute since the period of revolution is 10 minutes.

The wheel's direction of rotation—clockwise or counterclockwise—is not specified.

Let's look at both situations:

The present angle, assuming it spins clockwise, is equal to 270 – 36t degrees, where t is the duration in minutes.

Then the height function h = f(t)

= 28.5 + 22.5sin(a)

= 28.5 + 22.5sin(270 - 36t)

If the wheel rotates anti-clockwise, the current angle is

b = 270 + 36t degrees.

Then the height function

h = r(t)

= 28.5 + 22.5sin(b)

= 28.5 + 22.5sin(270 + 36t)

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Answer: 14

Step-by-step explanation:

The equation to find slope is y2-y1/x2-x1 or in simpler terms is rise over run.

We see that the y increase by 14 so the rise is 14 and the x is the same so the run is 0. So the slope is 14.

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By using the concept of reflection and scaling, it can be calculated that

New equation of parabola is [tex]y = -5x^2[/tex]

What is reflection and scaling?

Reflection is a mathematical transformation in which a mirror image of an object can be obtained without changing the shape and size of an object.

To draw an object of size proportional to the size of the original object, scaling is used

The equation of the parabola is [tex]y = x^2[/tex]

If it is reflected across x axis, its equation is [tex]y = -x^2[/tex]

Now  y  = -[tex]x^2[/tex] is scaled vertically by a factor of 5

New equation of parabola

[tex]y = -5x^2[/tex]

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The expression that results from applying the law of indices and expression is 5x^(-7/3).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

Here,

The resulted expression will be,

(125x)^(7/3)^(-1/3)

125=5^3

(a^n)^m = a^mn

(5x)^3^7/3^-1/3

(5x)^7*-1/3

5x^(-7/3)

The resulted expression will be 5x^(-7/3) using the law of indices and expression.

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Ms. Cole have the 8 pieces of string.

Given,

In the question:

A number line going from 0 to 4. numbers 0, 1, 2, 3, and 4 are marked on the line. marks divide the spaces between each number into 2 equal parts. Ms. Cole has 4 yards of string. she cuts the string into pieces that are each 1 2 yard long.

To find the how many pieces of string does Ms. Cole have?

Now, According to the question:

Total yards of string = 4

Length in yard of each string = 1/2 yards

Number of pieces of string Ms. Cole has :

Total. Yards of string / length in yard of each string

=> 4 / (1/2)

=> 4 * (2 /1)

=> 8/1

=> 8 pieces of string.

Hence, Ms. Cole have the 8 pieces of string.

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Answer:

1

Step-by-step explanation:

9/8.3 = 1.0843, rounded to the nearest whole number is 1

The average number of hours that Ashley worked per day is obtained as follows:

Mean = sum of relative frequencies x outcome

The relative frequency table shows that absolute frequencies of the number of hours worked, that is, the number of days in which each amount of hours was worked.

Then the relative frequencies are obtained by the division of each of the absolute frequencies by the total number of outcomes, which is the sum of all the relative frequencies.

Finally, the mean value is obtained just like the mean of a discrete distribution, with the multiplication of each outcome by it's relative frequency obtained previously.

The problem is incomplete, hence I gave a general pattern to find the mean of the data-set.

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Answer: -2

Step-by-step explanation: