Knowledge Check
Question 10
Keith purchased a prepaid phone card for $50.75. Calls cost 8 cents a minute using this card. The credit, C (in dollars), left on the card after it is used for x
minutes of calls is given by the following
C=50.75-0.08x
How much credit is left on the card after Keith uses it for 30 minutes of calls

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer:

-6

Step-by-step explanation:

It can be inferred that there is a statistically significant result if the confidence interval excludes the value of zero effect.

Confidence Interval;

In statistics, confidence is another word for probability. For instance, if you create a confidence interval with a 95% confidence level, you can be sure that 95 times out of 100 the estimate will fall between the upper and lower values indicated by the confidence interval.

Therefore,

The confidence level is 95% if your significance level is 0.05. The hypothesis test is statistically significant if the P value is lower than your significance (alpha) level. The findings are statistically significant if the confidence interval excludes the null hypothesis value. 0

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Answer:

P = 37 cm

A = 85 cm^2

Step-by-step explanation:

l = length, w = width, A = Area, P = Perimeter

l = 10 cm

w = 8.5 cm

A = l * w

P = 2l + 2w

Solve for Area:

A = 10 cm* 8.5 cm  ==> substitute l = 10 cm and w = 8.5 cm

A = 10 * 8.5 * cm * cm  ==> combine like terms

A = 85 cm^2

Solve for Perimeter:
P = 2(10 cm) + 2(8.5 cm)  ==> substitute l = 10 cm and w = 8.5 cm

P = 20 cm + 17 cm  ==> simplify

P = 37 cm

Answer:

3.56X10^-6

Step-by-step explanation:

In converting numbers to scientific notation, simply move the decimal point of the number until the numerical coefficient is greater than 1 but less than 10. Be sure to take note of the following:

1. The numerical coefficient.

2. Number of times we move the decimal point. It will be the exponent with the base of 10.

3. The direction we take in moving the decimal point. If the direction is to the right, take the negative sign for the exponent. If the direction is to the left, take the positive sign for the exponent.

Here, we move the decimal point of 0.00000356 to the right 6 times. So, we have now 3.56X10^-6.

Answer:Kurt’s ending balance on April 30 was $331.36. Add or subtract the items in his check register, shown below, to find his balance on May 30.DateTypeDescriptionAmount05/01Check #478Car payment$186.4705/05DebitGroceries$66.4205/08DepositPaycheck$279.6205/15DepositTax return$95.0205/29Check #479Insurance$160.00Assuming this record is complete, what is Kurt’s ending balance?a.$369.61b.$359.53c.$293.11d.$274.59

This the answ.er: $293.11. Which is C.

Step-by-step explanation:

The two factors of the quadratic polynomial x^2 + 3/2 x - 1 are:

(x - 2) and (x + 0.5)

We have a quadratic polynomial, sadly we don't have the options for the factors, so we will find the two factors of our polynomial.

To find the factors first we need to solve the quadratic equation:

x² + (3/2)*x - 1 = 0

Using the quadratic formula we get the solutions:

\(x = \frac{-3/2 \pm \sqrt{(3/2)^2 -4*1*(-1)} }{2*-1} \\\\x = \frac{-3/2 \pm 2.5 }{-2}\)

Then the two solutions are:

x = (-3/2 + 2.5)/-2 = -0.5

x = (-3/2 - 2.5)/-2 = 2

Then we can factorize our polynomial as:

p(x) = (x - 2)*(x - (-0.5))

p(x) = (x - 2)*(x + 0.5)

So the two factors are:

(x - 2) and (x + 0.5)

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Since the final score of a hockey game was 4 to 3, there must have been more than 100 different scores that could have been at the end of the first period.

Therefore, we can say that there were an infinite number of different scores that could have been at the end of the first period. The reason behind this is that there is no restriction on how many goals can be scored in any period of the game.The final score of a hockey game does not directly reflect the number of goals scored in any of the periods of the game, except for the last period. This means that there are multiple scores that are possible at the end of the first period in this case. It is also possible that there were no b at the end of the first period.

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Answer:

\(\fbox{height \: of \: prism = 19 \: mm}\)

Step-by-step explanation:

Given:

Shape of object is pentagonal prism

Side of pentagon= 12mm

Apothem of pentagon= 5 mm

Volume of pentagonal prism= 2,850 cubic mm.

To find:

Hieght of pentagon prism= ?

Solution:

To find height of prism it's necessary to calculate the surface area of base,

\(Area \: of \: regular\: pentagon = \frac{5}{2} \times side \: of \: pentagon \: \times apothem \\ Area \: of \: regular\: pentagon = \frac{5}{2} \times 12 \times 5 \\ Area \: of \: regular\: pentagon= \frac{5}{ \not2} \times \not12^{6} \times 5 \\ Area \: of \: regular\: pentagon= 5 \times 6 \times 5 \\ Area \: of \: regular\: pentagon= 150 \: {mm}^{2} \)

\(Volume \: of \: prism = surface \: area \: of \: base \: \times height (h) \\ 2850 = 150 \times h \\ h = \frac{2850}{150} \cdot \frac{ {mm}^{3} }{ {mm}^{2} } \\ h = \frac{\not{ {2850}^{19} }} {\not150} \cdot \frac{ {mm}^{\not {3}^{1} } }{ {mm}^{\not2} } \\ \fbox{h = 19 \: mm}\)

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The required height of the pentagonal prism is 19 cm                              

Given that,
A figure of a pentagon prism is shown with
The volume of the prism = 2850 cubic cm
Side of pentagon base = 12 mm.
And the perpendicular distance from the center to the side = 5 mm.

Volume is defined as the ratio of the mass of an object to its density.
Or in mathematics volume can be calculated as the area of the base multiplied by the height.

In order to get the height of the prism first, we have to calculate the area of the base and then divide the volume by its base area to get its height.

The base area = 5/2 * side * perpendicular height to side from center.
                         = 5 / 2 * 12 * 5
                         = 150
The volume of the prism = base area * height
                              2850 = 150 * height
                             height = 2850/15
                                         =  19 cm

Thus, the required height of the pentagonal prism is 19 cm                              

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Answer:

80?

Step-by-step explanation:

if there are 9 kids and every kid ends up with 8 pieces, then you do 8x9 which is 72. ut then you add 8 bc larson got his pieces.  so the answer is 80 im pretty sure

The length of midsegment of the trapizoid with bases 35 and 71 is 53.

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

A trapezoid is a closed, four-sided, two-dimensional shape that has both a perimeter and an area. The bases of the trapezoid are the two sides of the form that are parallel to one another. The legs or lateral sides of a trapezoid are the non-parallel sides. The altitude is the smallest distance between two parallel sides. Calculating a trapezoid's area is easy since its opposite sides are parallel to one another.

A trapezoid differs from other quadrilaterals in that it has the following characteristics:

The length of midsegment is sum of bases divided by 2

therefore midsegment = (35 + 71)/2 = 53.

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The simple interest equation that represent the situation is A = t/5

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest. For example, when a person takes a loan of 500 dollars, at a rate of 10 per annum for two years, the person's interest for two years will be S.I. on the borrowed money.

Principal(P) borrowed =  $2

Rate(R) in percentage = 10

time in years = t

Simple interest(A) = P X R X t / 100

A = 2 X 10 X t/ 100

After reducing 20/100 to the lowest term

A = t/5

In conclusion the simple interest(A) = t/5

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The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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When children create an imaginary town with various blocks and figurines, they are learning through play and engaging in important cognitive and social development processes.

1. Imagination and Creativity: Building an imaginary town involves using their imagination and creativity to create a world of their own. This helps children develop their cognitive skills by coming up with ideas, planning and problem-solving.

2. Language and Communication: During play, children may engage in pretend conversations and storytelling, which helps enhance their language skills and vocabulary. They may also negotiate and cooperate with others, improving their social communication skills.

3. Fine Motor Skills: Manipulating blocks and figurines requires the use of fine motor skills. Children practice hand-eye coordination, dexterity, and control while building and arranging their town.

4. Social Skills: Collaborating with others in creating the town encourages teamwork, sharing, and turn-taking. Children learn to negotiate, compromise, and solve conflicts, promoting social and emotional development.

5. Cognitive Development: Creating an imaginary town involves categorization, spatial awareness, and problem-solving skills. Children learn to organize and categorize blocks, create different structures, and explore cause-and-effect relationships.

In conclusion, when children engage in creating an imaginary town with blocks and figurines, they develop various skills such as imagination, creativity, language, fine motor, social, and cognitive skills. Through this play activity, children learn and grow in multiple ways, contributing to their overall development.

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The tree in Naomi's backyard lost 120 leaves in 12 days. Therefore, the required expression is A. 120÷12

Hope this helps :)

Answer:

Step-by-step explanation:

The answer is Samples. A sample is a random selection of members of a population. It is a smaller group drawn from the people with the entire population's characteristics.

I hope I have helped.

The inequalities x - 15 > 0 and x - 15 < 0 provide the conditions for which the function f(x) deviates from the limit L = 25.

The given limit statement is lim (x+10) = 25.

To write the inequalities f(x) - L, we need to express the difference between f(x) and the limit L, which is 25.

Step 1: Write the inequality f(x) - L > 0.

f(x) - L > 0

x + 10 - 25 > 0

x - 15 > 0

Step 2: Write the inequality f(x) - L < 0.

f(x) - L < 0

x + 10 - 25 < 0

x - 15 < 0

Therefore, the inequalities are x - 15 > 0 and x - 15 < 0.

Explanation:

The inequality x - 15 > 0 represents the condition where the difference between f(x) and L is positive, indicating that f(x) is greater than L (25). In other words, for values of x greater than 15, the function f(x) will be larger than 25.

On the other hand, the inequality x - 15 < 0 represents the condition where the difference between f(x) and L is negative, indicating that f(x) is less than L (25). In other words, for values of x less than 15, the function f(x) will be smaller than 25.

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Answer:

S₁₀ = - 838860

Step-by-step explanation:

the first term a₁ = 4

r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{4}\) = - 4

substitute these values into \(S_{n}\) , then

S₁₀ = \(\frac{4-4(-4)^{10} }{1-(-4)}\)

     = \(\frac{4-4(1048576)}{1+4}\)

     = \(\frac{4-4194304}{5}\)

     = \(\frac{-4194300}{5}\)

     = - 838860

Answer:

8x + 7y = 30 ( one solution)

8x - 7y = 2

-8x + 7y = -2 ( infinitely many solutions )

8x - 7y = 2

8x - 7y = 2

-8x + 7y = 2 ( zero solutions )

Answer:

Answer:

8x + 7y = 30 ( one solution)

8x - 7y = 2

-8x + 7y = -2 ( infinitely many solutions )

8x - 7y = 2

8x - 7y = 2

-8x + 7y = 2 ( zero solutions )

Step-by-step explanation:

Answer:

Plug in the variable (x) in the equation.

Step-by-step explanation:

once you plug it in, multiplied by two, and subtract by 3, and it should equal your y input

There are 356 hrs left to the trip.

534 hours are required to go from Washington to Boston \(dfrac13\) of the trip is already finished. The time remaining to complete the journey would then be \(dfrac23\)of the way. To get the number of hours left to the trip is shown below:

\(534 hours\) ×\(2/3\) \(=\frac{534}{3}\)

\(= (178)(3)(2)/3\)

\(=356 hrs\)

Boston, Massachusetts is roughly 450 miles southwest of Washington. There are numerous ways to travel from Boston to Washington, DC due to the proximity of the two cities, including via rail, airline, bus, and vehicle.

Your best option for getting from Boston to Washington, DC will depend on your individual needs, including how much time you want to spend on the road, your financial situation, and the specific points of origin and destination in each city. Flying will get you there the quickest, and because there are so many direct flights, it can also be relatively economical.

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Answer:

y = -2x - 3

Step-by-step explanation:

Answer:

y=(10×10)÷(1-2) =N

Step-by-step explanation:

y -is the numerical angle of triangle

10×10because the triangle have a ten angle

1-2 cause the line of triangle

Answer:

d ≥ −11

Step-by-step explanation:

Step 1: Add 5 to both sides.

−2d−5+5 ≤ 17+5

−2d ≤ 22

Step 2: Divide both sides by -2.

−2d/−2 ≤ 22/−2

d ≥ −11

The equation for the relationship between units of white paint, w, and units of black paint, b is 3w + b = 4g

The given parameters;

number of white paints, w = 3

number of black paint, b = 1

Let the number of gray paint = g

the total number of gray paint formed = 4 units

The equation that show the relationship between the two paints is given as;

3w:b = 4g

3w + b = 4g

Thus, the equation for the relationship between units of white paint, w, and units of black paint, b is 3w + b = 4g

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The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.

The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:

C = 0.0052 + 0.3(10) + 20

C = 0.0052 + 3 + 20

C = 23.0052

Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:

C' = 0.0052 + 0.3(Y + ΔY) + 20

C' = 0.0052 + 0.3Y + 0.3ΔY + 20

To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):

MPC = (C' - C) / ΔY

MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY

Simplifying the equation, we can cancel out the terms that don't involve ΔY:

MPC = (0.3ΔY) / ΔY

MPC = 0.3

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Answer:

(a - 1)(3p - 2)

Step-by-step explanation:

3p(a - 1) - 2(a - 1) ← factor out (a - 1) from each term

= (a - 1)(3p - 2)

Answer:

Step-by-step explanation:

Given:

ToFind:

Solution:

ATQ,

As we know that,

\(\implies\:\:x = \dfrac{mx_{2} + nx_{1}}{m + n}\)

\(\implies\:\:x = \dfrac{(a-b)3 + (a+b)2}{3+2}\)

\(\implies\:\:x = \dfrac{3a - 3b + 2a + 2b}{5}\)

\(\implies\:\:\red{x = \dfrac{5a - b}{5}}\)

Similarly,

\(\implies\:\:y = \dfrac{my_{2}+ny_{1}}{m+n}\)

\(\implies\:\:y = \dfrac{(a+b)3+(a-b)2}{3+2}\)

\(\implies\:\:y = \dfrac{3a+3b+2a-2b}{5}\)

\(\implies\:\:\red{y = \dfrac{5a+b}{5}}\)

Hence,

Coordinate of 0 is \(\blue{\bigg( \dfrac{5a-b}{5},\:\dfrac{5a+b}{5}\bigg)}\)

Answer:

Nelson's average speed was 8 miles per hour.

Step-by-step explanation:

To find Nelson's average speed, you need to divide the distance he traveled by the time it took him to travel that distance. In this case, Nelson traveled 20 miles in 2 1/2 hours, so his average speed was 20 miles / 2.5 hours = <<20/2.5=8>>8 miles per hour.

Answer:

8 miles per hour

Step-by-step explanation:

In order to find Nelson's average speed, we can set up a proportion. To solve for x, x being miles traveled in one hour.

\(\frac{20 miles}{2.5hours} =\frac{x miles }{1 hour}\)

x= 8

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