Solve the systems by substitution.
-6x - 2y = 26
7y+3=x

A 95.2% confidence interval in z-score is a range of values that is likely to contain the true population mean with a probability of 95.2%. The z-score for a 95.2% confidence interval is approximately ±1.97.

To calculate the 95.2% confidence interval in z-score, we can use the following formula:

CI = X ± z × (σ/√n)

where X is the sample mean, σ is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution table.

For a 95.2% confidence interval, the area in the tails of the standard normal distribution is 0.024 (0.5 - 0.952/2). Therefore, the critical z-value for a 95.2% confidence interval is approximately ±1.97.

This formula assumes that the sample follows a normal distribution, or that the sample size is large enough to satisfy the central limit theorem.

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The answer to the given question about probability of Bob's shop is option 7) 79.4%.

Out of 700 cars, 144 require more than one day to repair. So the number of cars that can be fixed in one day is

700 - 144 = 556.

The probability that the next car brought to the shop can be fixed in a day is the ratio of the number of cars that can be fixed in a day to the total number of cars:

probability = 556/700

= 0.794 or 79.4%

Therefore, the correct answer is option 7) 79.4%.

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is used to quantify the likelihood of an event occurring, and it is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probability theory is widely used in various fields, such as statistics, physics, economics, and finance, to make predictions and decisions based on uncertain or incomplete information. It provides a powerful tool for analyzing and understanding uncertainty, risk, and randomness in real-world situations, and it has numerous practical applications in diverse areas of research and industry

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Hence, there is a 1/10 or 0.1 chance that both of the chosen kids will be under 62 inches tall.

In the field of mathematics known as probability, random chance and their results are examined. It entails putting a number between zero and 1, where 1 indicates that now the event is guaranteed to happen and 0 that it is impossible, to reflect the possibility of an event occurring. From straightforward games of chance to intricate real-world systems like share prices and weather patterns, probability theory offers a framework for the analysis and modelling of a wide range of phenomena. It has uses in physics, economics, computer science, statistics, and other disciplines.

given

Let A represent the scenario in which the first student chosen is under 62 inches, and B represent the scenario in which the second student chosen is under 62 inches as well.

Since there are two shorter kids out of a total of five students, the likelihood of choosing one on the first try is 2/5.

Given that the first student was shorter, the likelihood of choosing another shorter student on the second try is 1/4 because there would only be 1 shorter student left out of the other 4 students.

Thus, the likelihood of picking two consecutive students who are shorter

The formula for P(A and B) is P(A) P(B|A) = (2/5) (1/4) = 1/10.

Hence, there is a 1/10 or 0.1 chance that both of the chosen kids will be under 62 inches tall.

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Answer: 384 cm cubed

Step-by-step explanation: The first thing you will do is 48 square centimeters times 8 cm. Since 48 is squared you have that 2 right above it. Your 8 technically has a 1 above it. So add the 2 and the 1, and you will get cubed. (AKA 3)

The difference in centigrade degrees between a temperature of 60°F and a temperature of 78°F is 10°C.

To convert Fahrenheit (°F) to Celsius (°C), you can use the following formula:

°C = (°F - 32) / 1.8

Using this formula, we can first convert 60°F to Celsius:

°C = (60°F - 32) / 1.8

°C = (28°F) / 1.8

°C = 15.56°C

Similarly, we can convert 78°F to Celsius:

°C = (78°F - 32) / 1.8

°C = (46°F) / 1.8

°C = 25.56°C

The difference in Celsius degrees between these two temperatures is:

Δ°C = 25.56°C - 15.56°C

Δ°C = 10°C

Therefore, the difference in centigrade degrees between a temperature of 60°F and a temperature of 78°F is 10°C.

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There are approximately 78 trees on each acre of land when the trees are spread out evenly.

To find the number of trees on each acre of land mathematically, we can use the formula for average or mean.

The average number of trees per acre can be found by dividing the total number of trees by the total number of acres. In this case, we have 2808 trees and 36 acres:

Average number of trees per acre = Total number of trees / Total number of acres

Average number of trees per acre = 2808 / 36

Average number of trees per acre = 78

Therefore, there are approximately 78 trees on each acre of land when the trees are spread out evenly.

This means that if the land is divided into 36 equal sections, each section will have approximately 78 trees.

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According the given question 3A - 2B matrix is equal to:

[tex]\left[\begin{array}{ccc}10 & -5 & 3 &5 & -5 & 1\end{array}\right][/tex]

A matrix is a rectangular array οf numerical values, symbοls, οr verbal expressiοns that are οrganised in rοws and cοlumns. In many disciplines, such as cοmputer science, engineering, physics, and mathematics, it is used tο represent data.

Calculating 3A and 2B first, then deducting 2B frοm 3A, is required tο find 3A - 2B.

Calculating 3A:

[tex]3A = 3 * \left[\begin{array}{ccc}2 & -1 & 3\1 & 1 & -3 & -1\end{array}\right]= \left[\begin{array}{ccc}6 & -3 & 9\3 & 3 & -9 & -3\end{array}\right][/tex]

Calculating 2B:

[tex]2B = 2 * \left[\begin{array}{ccc}-2 & 1 & 3 & -1 & -2 & -2 \end{array}\right]= \left[\begin{array}{ccc}-4 & 2 & 6 & -2 & -4 & -4\end{array}\right][/tex]

Nοw, we can find 3A - 2B by subtracting 2B frοm 3A:

[tex]3A - 2B = \left[\begin{array}{ccc}6 & -3 & 9 &3& -9 & -3\end{array}\right] - \left[\begin{array}{ccc}-4 & 2 & 6 &-2 & -4 & -4\end{array}\right]= \left[\begin{array}{ccc}10 & -5 & 3 &5 & -5 & 1\end{array}\right][/tex]

Therefore, 3A - 2B is equal to:

[tex]\left[\begin{array}{ccc}10 & -5 & 3 &5 & -5 & 1\end{array}\right][/tex]

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Answer: The actual answer is 7/12, but the closest match is (A) 1/2.

The  price (in cents) should he charge for each of the remaining candy bars 49

First, we would want to calculate how much the box would sell for before the sister ate some.

We would get 24*63(in cents) and we can further get 1512 cents before the sister ate the candy bars.

The sister ate 7 candy bars leaving us with 31 candy bars. To deduct the price for each candy bar, it would be a situation like the following:

$6 for 3 boxes of 500 cookies (i know that's cheap)

6/3...

$2 per box.

Using our situation we get 1512 cents for 31 candy bars.

1512÷31

=48.77

That does seem unrealistic, so we round to the nearest whole number and we get...

49 cents

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the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55% is 0.29 = 29%

A binomial experiment is an experiment that has the following four properties:

The experiment consists of n repeated trials

Each trial has only two possible outcomes

The probability of success, denoted p, is the same for each trial

Each trial is independent

the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55%

We know that the binomial distribution

[tex]^nc_rp^rq^{n-r[/tex]

Where n is the number of trails

p is the probability of success in each trial

q =1-p which is the probability of failure

Here r=4

n=7

p= 55 % =0.55

then by the formula

[tex]p(4)=^7c_4(o.55)^4(0.45)^3\\\\p(4)=35*0.091*0.091\\p(4)=0.29[/tex]

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The cost of a Broadway show ticket in 2014, based on inflation, would be approximately $52.59.

Inflatiοn, in general, is the prοcess thrοugh which mοney lοses value οver time. As a result, 100 dοllars suddenly have less purchasing pοwer than they had previοusly. This indicates that the awards will increase tο maintain a steady purchasing pοwer.

Tο find the cοst οf a Brοadway shοw ticket in 2014, we need tο adjust the price frοm 2002 using the Cοnsumer Price Index (CPI) fοr each year. The CPI measures the changes in the cοst οf gοοds and services οver time due tο inflatiοn.

Here is the CPI data for the relevant years:

2002 CPI: 179.9

2014 CPI: 236.7

To adjust the 2002 price of $40 to its equivalent in 2014 dollars, we can use the following formula:

Adjusted Price in 2014 Dollars = Price in 2002 Dollars x (CPI in 2014 / CPI in 2002)

Plugging in the numbers, we get:

Adjusted Price in 2014 Dollars = $40 x (236.7 / 179.9) = $52.59

Therefore, the cost of a Broadway show ticket in 2014, based on inflation, would be approximately $52.59.

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Complete question:

In 2002 you could buy a Broadway show ticket for $40. Use the CPI chart below to find the cost of Broadway show in 2014 based on inflation.

Answer:

∠A = 48.2

Step-by-step explanation:

Cos^-1(6/9

Use the Cosine with the negative one because you are finding an angle. Then, because Cosine is adjacent/hypotenuse, 6 would be your adjacent side length to theta and 9 would be the hypotenuse as it is across from the right angle.

Answer:

The area is (9^2)π = 81π.

After descending [tex]21.5[/tex] feet, the scientist's new position in the submarine would be  [tex]30.8[/tex] feet below sea level.

The scientist was initially in a submarine, located 52.3 feet below sea level. This means that her position was  [tex]52.3[/tex]feet lower than the surface of the sea.

Over the next ten minutes, the scientist descended further into the ocean by [tex]21.5[/tex] feet. This means that she traveled down an additional [tex]21.5[/tex]feet from her initial position.

To calculate her new position below sea level, we can subtract the distance she traveled downward (21.5 feet) from her initial position (52.3 feet below sea level).

[tex]52.3 feet - 21.5 feet = 30.8 feet[/tex]

Therefore, after descending 21.5 feet, the scientist's new position in the submarine would be 30.8 feet below sea level.

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a) The plumber should buy 13 sections of 6-meter lengths of PVC pipes.

b) Assuming that there are no errors, the left-over pipe after satisfying Jobs A and B should be 3 meters.

We can use mathematical operations of addition, division, multiplication, and subtraction to determine the two quantities above.

In the first place, the total quantity of PVC pipes required is 75 meters.

This sum is divided by 6 to obtain the sections required, which is approximated to the nearest whole number.

Finally, 75 meters are subtracted from the total quantity bought.

PVC pipes required by Job A = 45 meters

PVC pipes required by Job B = 30 meters

The total quantity of PVC pipes required = 75 meters

The length of each PVC pipe = 6 meters

The number of pipes to buy = 13 sections (75 ÷ 6)

13 sections of pipes = 78 (6 x 13)

Leftover PVC pipes = 3 meters (78 - 75)

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To prove: Area of triangle MAP = 1/2 area of trapezium MNOP

Given: MN//OP and A is the midpoint of NO

Proof:

Let h be the height of trapezium MNOP.

The area of trapezium MNOP is given by:

Area of trapezium MNOP = (1/2) × (MN + OP) × h

Since MN//OP, we have MN = OP.

Therefore, Area of trapezium MNOP = (1/2) × 2MN × h = MN × h

Now, consider triangle MAP.

The base of triangle MAP is MA, which is half of NO.

Therefore, the base of triangle MAP is (1/2) × NO.

The height of triangle MAP is h, which is the same as the height of trapezium MNOP.

Therefore, the area of triangle MAP is given by:

Area of triangle MAP = (1/2) × (base) × (height) = (1/2) × (1/2NO) × h

Substituting NO = 2OA, we get:

Area of triangle MAP = (1/2) × (1/2 × 2OA) × h = (1/2) × OA × h

Since A is the midpoint of NO, we have OA = 1/2NO.

Therefore, Area of triangle MAP = (1/2) × (1/2NO) × h = (1/2) × (base of trapezium MNOP) × h

Hence, Area of triangle MAP = 1/2 Area of trapezium MNOP.

Therefore, the given statement is proved.

Answer: Given that MNOP is a trapezium with MN parallel to OP and A is the midpoint of NO.

To prove that the area of triangle MAP is half the area of trapezium MNOP, we need to use the following theorem:

Theorem: If a line segment joins the midpoint of one side of a triangle to a vertex opposite to that side, then the segment divides the triangle into two equal areas.

Proof:

Since A is the midpoint of NO, we can draw a line segment AP from vertex P to point A on NO as shown in the figure below:

css

Copy code

      M _______N

       |\      |

       |  \    |

       |    \  |

       |      \|

      O--------P

            A

We can see that triangle MAP is formed by the line segment AP and side MP of the trapezium.

Also, we can see that triangle MAN is congruent to triangle NOP because they are both right triangles with corresponding sides parallel. Therefore, they have the same area.

Since MNOP is a trapezium, the area of trapezium is given by:

Area of trapezium MNOP = (1/2)(MN+OP) × height

Since MN is parallel to OP, the height of the trapezium is the same as the height of triangle MAN and NOP.

Therefore, the area of trapezium MNOP can be written as:

Area of trapezium MNOP = (1/2)(MN+OP) × height

= (1/2)(MA+AP+OP) × height

= (1/2)(MA+MP) × height (Since AP = NO/2 = height)

So, we have proved that:

Area of trapezium MNOP = (1/2)(MA+MP) × height

Using the theorem, we know that AP divides triangle MAP into two equal areas. Therefore,

Area of triangle MAP = (1/2) × Area of triangle MAP

Substituting the above in the expression for the area of trapezium, we get:

Area of trapezium MNOP = Area of triangle MAP + (1/2) × Area of triangle MAP

= (3/2) × Area of triangle MAP

Therefore, we have:

Area of triangle MAP = (1/2) × Area of trapezium MNOP

Thus, we have proved that the area of triangle MAP is half the area of trapezium MNOP.

Step-by-step explanation:

Answer:

A. 13.125cm

Step-by-step explanation:

To solve for the width of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is:

volume = length x width x height

We are given that the volume is 6,142.5 cm^3, the height is 16.25 cm, and the length is 28 cm. Let's substitute these values into the formula and solve for the width:

6,142.5 cm^3 = 28 cm x width x 16.25 cm

Dividing both sides by (28 cm x 16.25 cm), we get:

width = 6,142.5 cm^3 / (28 cm x 16.25 cm)

= 13.125 cm

Therefore, the width of the rectangular prism is 13.125 cm. So, the correct answer is A) 13.125 cm.

Answer:

[tex]b = - 0.3125[/tex]

Step-by-step explanation:

[tex]8b - 1 = 24b + 4[/tex]

Collect like-terms (also, when moving a term to the other side, its sign changes to the opposite of the previous one):

[tex]8b - 24b = 4 + 1[/tex]

[tex] - 16b = 5[/tex]

Divide both sides of the equation by (-16) to make b the subject:

[tex]b = - 0.3125[/tex]

Answer:

c. greater than​

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] + [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{6}[/tex] + [tex]\frac{4}{6}[/tex] = [tex]\frac{7}{6}[/tex] ≈ 1.167

1.167 > 1

So, the answer is c. greater than​

The measure of the angle in the given circle which pass through 2 parts out of 5 is 144°.

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The radius of a circle is the separation between any point on the circle and its center.

The radius must typically be a positive integer. A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior.

In common usage, the word "circular" can be used to describe both the figure's edge and its entirety, including its interior.

So, we know that:

The angle of the center of the circle is 360°.

We also know that in the given situation, the circle is divided into 5 parts.

Then,

= 360/5

= 72

Now,

The measure of 2 parts:

72 + 72 = 144

Therefore, the measure of the angle in the given circle which pass through 2 parts out of 5 is 144°.

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Answer:

To determine if (0,3) is a solution to y>2, we need to check if y is greater than 2 when x=0 and y=3. Since 3 is greater than 2, the point (0,3) satisfies the inequality y>2.

To graph the inequality y>2, we need to shade the region above the horizontal line y=2. The line y=2 is a solid line since it includes the points where y=2, but the region above the line is shaded with a dashed line since it does not include the points where y=2.

Here is a description of the graph:

Draw a horizontal line passing through the point (0,2).

Shade the region above the line with a dashed line.

The graph visually represents all the points that satisfy the inequality y>2. Since the point (0,3) is above the line, it is part of the shaded region and satisfies the inequality.

Answer:

Step-by-step explanation:

The sketch is a right-angled triangle.

We can use Pythagoras' theorem.

[tex]z^{2} =x^{2} +y^{2}[/tex]

z=√(50^2+25^2)

z= 25√5

z=25*2.23

z=55.75

z≈56km

the distance between where he started the

journey=56km

tan(90-Θ)=25/50

cotΘ=1/2

tanΘ=2

Θ=[tex]tan^{-1} (2)[/tex]

bearing of his starting point from his end point[tex]tan^{-1} (2)[/tex]

Answer:

Step-by-step explanation:

[tex]T_{r+1}=nc_{r}x^{n-r}a^r\\x=v\\a=-w^2\\n=22\\r+1=15\\r=15-1=14\\22c_{14}=22c_{22-14}=22c_{8}\\ T_{15}=22c_{8}v^{22-14}(-w^2})^{14}\\T_{15}=22c_{8}v^8w^{28}[/tex]

he expression 4(3x=2)-9 can be written as 12x - 9. I

the area of the shape shown in the diagram is 91 m².

Area is the space bounded by a plane shape.

To calculate the area of the shape, we use the formula below

Note: Area of the shape = Area of the rectangle+ Area of the triangle

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area is 91 m².

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The equation of a circle given by the graph is (x-3)²+(y+2)²=29,

hence option b is correct.

A circle is a closed curve that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center. A circle with an (h, k) center and a radius of r has the equation:

(x-h)² + (y-k)²= r²

This is the equation's standard form. Hence, we can quickly determine the equation of a circle if we know its radius and center coordinates.

We know that the equation of the circle is -

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where (h,k) is the center of the circle and r is the radius,

given that,

center of the circle is = (3,-2)

and the radius is=√29

Hence the equation of a circle is

[tex](x-3)^2+(y+2)^2=(\sqrt29)^2\\\\(x-3)^2+(y+2)^2=29[/tex]

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The value of m∠N is 21° ,the value of m∠M is 55° and the value m∠O is 106°.

To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore:

m∠M + m∠N + m∠O = 180

Substituting the given angle measures, we get:

(4x-13) + (2x-13) + (5x+19) = 180

Simplifying the equation, we get:

11x - 7 = 180

11x = 187

x = 17

Now that we know the value of x, we can find the measure of each angle. Substituting x = 17, we get:

m∠M = (4x-13) = (417-13) = 59 degrees

m∠N = (2x-13) = (217-13) = 21 degrees

m∠O = (5x+19) = (5*17+19) = 106 degrees

Therefore, the measure of ∠MNO is:

m∠N = 21 degrees

Note: The question also asks for the measure of ∠P, but there is no information given about ∠P in the problem.

In AMNO, m angle M = (4x - 13) deg m angle N = (2x - 13) deg and m angle O = (5x + 19) deg Find m/N.

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the equation to find the discount for oranges is: [tex]r = 3.89 + 2.49[/tex]  [tex]r= 6.38[/tex]

The discount for apples is $ [tex]2.89[/tex] + $ [tex]1.49[/tex], since you can get another bag for $1.49 when you buy a 5-pound bag of apples at the regular price.

So the equation to find the discount for apples is:

[tex]a = 2.89 + 1.49[/tex]

[tex]a = 4.38[/tex]

Similarly, the discount for oranges is $ [tex]3.89[/tex] + $ [tex]2.49[/tex], since you can get another bag for $2.49 when you buy a 5-pound bag of oranges at the regular price.

Therefore, the equation to find the discount for oranges is: [tex]r = 3.89 + 2.49[/tex]

[tex]r = 6.38[/tex]

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Answer:

modes

Step-by-step explanation:

The only one of the three (median, mode, mean) that there can be more than one for a set is the mode, and in fact it has two modes: 5 and 9.

Answer: modes

The random variable x is normally distributed with mean u=89 and standard deviation o=4. The indicated probability, ​P(x<8​7)= 0.3085.

In statistics, standard deviation is a measure of the amount of variation or dispersion in a set of data. It is a commonly used measure of the spread of a distribution and is calculated as the square root of the variance.

A higher standard deviation indicates that the data points are more spread out from the mean, while a lower standard deviation indicates that the data points are more tightly clustered around the mean.

Standard deviation is an important concept in statistics and is used in many statistical analyses, such as hypothesis testing and confidence interval estimation. It is also used in finance and economics to measure the risk associated with investments and to assess the variability of economic data.

To solve this problem, we need to standardize the value using z-score formula.

z = (x - mu) / sigma

Here, x = 87, mu = 89, and sigma = 4.

z = (87 - 89) / 4 = -0.5

We can look up the corresponding area under the standard normal distribution curve using a table or calculator. The area to the left of z = -0.5 is 0.3085.

Therefore, P(x < 87) = P(z < -0.5) = 0.3085.

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