Find the largest rational number r for which 5r ≤ 33.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Select the equation that passes through (-2,1) and has slope 3

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Formula used, here [tex]\bf{y-y1=m(x-x1)}[/tex]

[tex]\bf{y-1=3(x-(-2)}[/tex] | put in the values, then, simplify

[tex]\bf{y-1=3(x+2)}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=y-1=3(x+2)}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1\theta l}}[/tex]

∞

Using the t-distribution, the 98% confidence interval for the mean of the population is (99.21, 110.79).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

Researching the problem on the internet, the data-set is given as follows:

104, 102, 103, 105, 125, 106, 107, 110, 110, 95, 108, 86, 112, 101, 101.

The parameters are given as follows:

[tex]\overline{x} = 105, s = 8.54, n = 15[/tex].

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 15- 1 = 14 df, is t = 2.6245.

Hence the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 105 - 2.6245\frac{8.54}{\sqrt{15}} = 99.21[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 105 + 2.6245\frac{8.54}{\sqrt{15}} = 110.79[/tex]

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Answer:

152 miles

Step-by-step explanation:

380/5 = 76

76*2 = 152

as they will have traveled 2/5, you would need to divide your miles by 5 then multiply by 2!

The distance from Platform B to Platform C is 26.926 units

The given parameters are;

The zip-line course distance from platform A to platform F is given;

On the given graph of the path of travel we have;

Coordinates of the point B = (-25, -20) and the coordinates of the point C = (-15, 5).

The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula

[tex]l=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Therefore, the distance between B and C is found by substituting (-25, -20) = (x₁, y₁) and (-15, 5) = (x₂, y₂)

Which gives

[tex]l=\sqrt{(5-(-20))^2}+((-15)-(-25))^2\\l=26.926 units[/tex]

The distance from points B to C = 26.926 units. The distance from Platform B to Platform C is 26.926 units.

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The approximate APR for the purchase is 16%

To calculate the annual percentage rate (APR)

We would calculate the interest rate

Add the administrative fees to the interest amount

Divide the loan amount (principal)

Divide by the total number of days in the loan term

Multiply all year

Multiply by 100 to convert to a percentage

Interest= P * R * t

APR= [tex]\frac{\frac{216}{900}}{6 * 4 * 100}[/tex]

APR = 16%

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The measure of <TRS and angle d are 70 and 43degrees respectively

The given triangles are isosceles triangles since they have two equal sides.

14) From he triangle RST

<TRS + 90 + 20 = 180

<TRS + 110. = 180

Subtract 110 from both sides

<TRS = 180 -110

<TRS = 70 degrees

15) For this triangle;

d = 86/2

d = 43 degrees

Hence the measure of <TRS and angle d are 70 and 43degrees respectively

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The computation shows that the amount will be:

Jonah earns $12.50 per hour

He works for 4.5 hours

Amount he earned will be:

= 12.50 × 4.5 = $55.25

Items worth is $41.23

Amount paid is $50.23

Extra amount paid will be:

= 50.23 - 41.23

= $9

Length of cloth available is 20 m

Length of one long-sleeved blouse is 2.5m

Number of blouses that can be made will be:

= 20/2.5 = 8

Potatoes weight is 3.2 pounds

Oranges weight is 2.3 pounds

Onions weight is 2.7 pounds

Total weight of the purchase will be:

= 3.2 + 2.3 + 2.7 = 8.2 pounds

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Complete question:

Match each problem to its solution. 8 8.2 9 56.25 Jonah earns $12.50 per hour as a marketing intern. If he works for 4.5 hours, how many dollars does he earn? arrowRight Jessica purchased items worth $41.23 at the local grocery store. The cashier made a mistake while ringing up her items, and Jessica ended up paying $50.23. How many extra dollars did she pay? arrowRight Josie has 20 meters of cloth. She needs to make long-sleeved blouses with that cloth. If one long-sleeved blouse requires 2.5 meters of cloth, how many blouses can she make with the material? arrowRight Jeremy bought 3.2 pounds of potatoes, 2.3 pounds of oranges, and 2.7 pounds of onions. How many pounds does his purchase weigh? arrowRight

Answer:

Area = 1125mi

Step-by-step explanation:

Area of sector =  [tex]r^2 *\frac{\alpha }{2}[/tex]

[tex]r^{2} =5^{2} =25[/tex]

[tex]25*\frac{\alpha}{2}[/tex]

[tex]25*\frac{90}{2} =25*45=1125[/tex]

[tex]\alpha[/tex] = angle

[tex]r[/tex] = radius

radius is 5mi

in this case the angle is 90°

A = 1125mi

you can also solve by using circle area which is [tex]\pi r^{2}[/tex]

then divide by 4 because this is 1/4 of the circle.

Hope this helps

Triangle ABC was translated using the rule (x, y) (x + 2, y + 1) to form congruent triangle A'B'C' with AA' = √5 units

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Point A is at (0, 0). Using the transformation T: (x, y) (x + 2, y + 1), point A' = (2, 1). Hence:

[tex]AA'=\sqrt{(1-0)^2+(2 - 0)^2}=\sqrt{5}[/tex]

Triangle ABC was translated using the rule (x, y) (x + 2, y + 1) to form congruent triangle A'B'C' with AA' = √5 units

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[tex]\huge\boxed{3.81\ \text{centimeters}}[/tex]

We simply need to convert 1.5 inches to centimeters.

Use multiplication:

[tex]1.5\cdot2.54=\boxed{3.81}[/tex]

The rule of the points is y = 3.2x - 0.7

The points are given as:

(-2,-7) (0,-1) (7, 22)

The above points form an approximate linear equation.

So, we make use of a linear regression to determine the rule

When the above points are entered in a statistical calculator, we have the following summary:

The regression equation is then represented as:

y = bx + a

Where

b = SP/SSX = 144.67/44.67 = 3.23881

a = MY - bMX = 4.67 - (3.24*1.67) = -0.73134

This gives

y = 3.23881x - 0.73134

Approximate

y = 3.2x - 0.7

Hence, the rule of the points is y = 3.2x - 0.7

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The area of the triangle is 14.1 square meters

The side lengths are given as:

5m, 6m and 9m

Calculate the semi-perimeter (s) using

s = (5 + 6 + 9)/2

Evaluate

s = 10

The area is then calculated as:

[tex]Area = \sqrt{s(s -a)(s-b)(s-c)[/tex]

This gives

[tex]Area = \sqrt{10 * (10 -5)(10-6)(10-9)[/tex]

Evaluate the products

[tex]Area = \sqrt{200[/tex]

Evaluate the exponent

Area = 14.1

Hence, the area of the triangle is 14.1 square meters

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Unit conversion is a way of converting some common units into another without changing their real value. The lemonade left with Tony is 4500ml.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

One litre is equal to 1000 millilitres. Tony made 14 Liter of lemonade, therefore, Tony made 14,000 millilitres of lemonade. His guest drank 9500 millilitres. Therefore, the lemonade left with Tony is,

Lemonade left = 14,000 - 9,500 = 4,500 ml

Hence, the lemonade left with Tony is 4500ml.

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[tex](x+3)^3\cdot x\cdot (x-3)=(x^3+9x^2+27x+27)\cdot (x^2-3x)=\\=x^5-3x^4+9x^4-27x^3+27x^3-81x^2+27x^2-81x=\\=x^5+6x^4-54x^2-81x[/tex]

Answer:

[tex]B: \frac{1}{2}[/tex]

Step-by-step explanation:

Plug 1 in as t

[tex]F(1) = 4 * \frac{1}{2^{3(1)}}[/tex]

Simplify the exponent 3*1

[tex]F(1) = 4 * \frac{1}{2^{3}}[/tex]

Cube the 2

[tex]F(1) = 4 * \frac{1}{8}[/tex]

Multiply:

[tex]F(1) = \frac{4}{8}[/tex]

Simplify:

[tex]F(1)=\frac{1}{2}[/tex]

The probability that at least one of the calculators is defective is : 0.725

Probability is the likelihood of an event happening or not.

if there is certainty that the event would happen probability is 1.

Analysis:

probability = required outcome/possible outcome

for 33 good calculators and 12 defective calculators, total calculators = 45

4 calculators were chosen, possible outcome = 45C4 = 148995

Required outcome = 33C3 . 12C1 + 33C2 . 12C2 + 33C1 . 12C3 + 33C0 . 12C4

= 65472 + 34848 + 7260 + 495 = 108075

Probability = 108075/148995 = 0.725

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The function with the same end behavior of f(x) is the last option:

[tex]g(x) = (-\frac{1}{3} )*x[/tex]

By looking at the graph, we can see that the end behavior of f(x) is:

as x → ∞; f(x) → -∞

as x → -∞; f(x) → ∞

Then we just want a function that depends linearly with x and that has a negative coefficient.

The correct option is the last one:

[tex]g(x) = (-\frac{1}{3} )*x[/tex]

Where clearly, when x tends to infinity the function tends to negative infinity, and when x tends to negative infinity, the function tends to infinity.

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The  composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.

A translation can be explained as the movement of a shape in a direction which could be up, down but the appearance of the figure remain unchanged in any other way.

And from the figure, we can see that a translation is used, because of the movement of EFGH to figure E"F"G"H" which occurred in the same direction.

Hence,  composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.

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Where are the options?

Answer:

system

equations

Step-by-step explanation:

Answer:

A system of two linear equations can have one solution, an infinite number of solutions, or no solution.

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

Explanation:

An equation is something like [tex]\text{y} = 2\text{x}+5[/tex] and [tex]\text{y} = 3\text{x}+7[/tex]

When we combine two such equations to form a group (of sorts), we consider this to be a system of equations.

We use a single curly brace to write the system

[tex]\begin{cases}\text{y} = 2\text{x}+5\\\text{y} = 3\text{x}+7\end{cases}[/tex]

Here are the three cases mentioned when it comes to solutions.

Side note:  Any solution is of the form (x,y)

(a) By the formula for the area of a square, the answer is [tex]16^2 = 256[/tex] square km

(b) By the formula for the area of a circle, the answer is [tex](\pi)\left(\frac{16}{2} \right)^2 =64\pi[/tex] square km

(c) Subtracting areas, we get [tex]256-64\pi[/tex] square km

Answer: d

Step-by-step explanation:

60*0.6=36

60-36=24

24 are not thoroughbreds

Using the normal distribution, it is found that there is a 0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 100, \sigma = 15[/tex].

The probability that the person has an IQ score between 92 and 108 is the p-value of Z when X = 108 subtracted by the p-value of Z when X = 92, hence:

X = 108:

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

[tex]Z = \frac{108 - 100}{15}[/tex]

Z = 0.53

Z = 0.53 has a p-value of 0.7019.

X = 92:

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

[tex]Z = \frac{92 - 100}{15}[/tex]

Z = -0.53

Z = -0.53 has a p-value of 0.2981.

0.7019 - 0.2981 = 0.4038.

0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.

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The conclusion that is justified based on the research is that he rejected the null hypothesis that women drank the same amount of water per kg of body weight per day as men.

It should be noted that a research is simply used to get information about a topic.

In this case, it can be deduced that a type 1 error is committed. This implies the rejection of the null hypothesis when it's true.

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Answer:

Two

Step-by-step explanation:

Solutions are when the two graphs intersect

Answer:=102.5

Step-by-step explanation:

Option B and D would have closed circles when graphed

The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function.

At the endpoints of the domain, we draw open circles to indicate where the endpoint is not included because of a less-than or greater-than inequality; we draw a closed circle where the endpoint is included because of a less-than-or-equal-to or greater-than-or-equal-to inequality.

∴ Option B and D that are 5.7 ≤ p and [tex]\frac{1}{2}[/tex] ≥ y respectively would have closed circles

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Using the Empirical Rule, it is found that 49 farms in the sample have land and building values per acre between $1100 and $1700.

It states that, for a normally distributed random variable:

Considering the given mean and standard deviation, values between $1100 and $1700 are within 1 standard deviation of the mean, which is a percentage of 68%.

Hence, the number of farms out of 72 is:

0.68 x 72 = 49 farms.

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Answer:

C

Step-by-step explanation:

The sum of Sonya's 5 initial tests = 89*5 = 445.

445 + 95 = 540 (sum of the 6 tests)

Average = 540/6 = 90

Hence C

Answer:

C.  90.00

Step-by-step explanation:

We find average by adding up all values in a data set and dividing by the total number of values we have

We can say that Sonya got 89 for each test (it doesn't matter what each test score exactly was--you'll see why in a second)

So, we can add up 89 five times (5 tests have occured)

*I say add up, because that's what average is, but you can find this number by multiplying 89 · 5

89 · 5 = 445

(89 + 89 + 89 + 89 + 89 = 445)

Now, we need to add up our new value: 95

445 + 95 = 540

So, we can now divide 540 (sum of all values) by 6 (total number of values)

540 ÷ 6 = 90

So, C (90.00) is her new average

hope this helps! have a lovely day :)

Answer:

A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too. For example, 9x3yz is a single term, where 9 is the coefficient, x, y, z are the variables and 3 is the degree of monomial.