Solve by using substitution. x+2y=−1 x=y+5

Peggy completed more of the math homework than Al

What does division of fractions mean?

A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.

we know that

In order to be able to compare fractions more easily it is recommended that both have the same denominator

Peggy

5/6 x 5 = 25/30

Al

4/5 x 6 = 24/30

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The finding is significant at both α = 0.05 and α = 0.01.

What is hypothesis ?

A hypothesis (plural: hypotheses), in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

Have given ,

H0: p = 0. 65 ,  Ha: p < 0. 65 and  the z test statistic is found to be -2. 35.

From the test statistic value, we can obtain the p value of the test ,

To determine if the claim is significant at both α = 0.05 and α = 0.01

We compare the Z statistic and Z critical values

If Z statistic < Z critical ; then we reject H0; if otherwise, we fail to reject H0

Z critical at 95% one tailed = - 1.645 (left tail)

Z critical at 95% one tailed = -2.326 (left tail)

- 2.35 < - 1.645

-2. 35 < 2.326

Since, Z statistic < Z critical;

The finding is significant at both α = 0.05 and α = 0.01.

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If Alice tests positive and the experts are right on the population prevalence, the probability that Alice has the disease is 0.489.

In the given question, a new disease has been observed, and experts believe that 1% of the population have it.

A test is developed that has 95% true positive rate and 1% false positive rate.

From the given data,

Let E be the event that a patient has a disease and F be the event that a patient has tested positive.

Then according to Bayes' theorem we have,

P(E/F) = P(E)P(E/F)}/(P(E)P(E/F)+P(E')P(F/E')

P(E/F) = (1*95)/(1*95)*(99*1)

P(E/F) = 95/194

P(E/F) = 0.489 (approx.)

Hence, the probability that Alice has the disease 0.489.

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The potential instances of sample distribution are options C and E.

Option E. Average male height based on samples of size 30.

Option C. Mean trout lengths based on samples of size 5.

The sampling distribution of the mean is the distribution of the variable x (all feasible sample means of size n) for a variable x and a given sample size n.

The mean is the most typical kind of sample distribution. Plotting the data points and computing the means of each sample group drawn from the population are its main goals.

This idea, which is a form of the probability distribution, is frequently used to gather precise data from a sizable population that is divided into a number of randomly chosen samples. This idea is further divided into three categories: T-Sampling, proportional sampling, and the sampling distribution of the mean.

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The correct questions should be like this:

Which of the following are possible examples of sampling distributions? (Select all that apply.) average SAT score of a sample of high school students

all mean trout lengths in a sampled lake

mean trout lengths based on samples of size 5

heights of college students at a sampled university

average male height based on samples of size 30

The volume of the prism is 103.32 cubic inches (optionD)

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.

The base area of the prism = 4.1×7.2 = 29.52 inches squared.

The height of the prism is 3.5 inches

Therefore volume = base area × height

volume = 29.52× 3.5 = 103.32 cubic inches.

Therefore the volume of the shape is 103.32 cubic inches.

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Answer: The odds in favor of an event happening are the ratio of the probability of the event happening to the probability of the event not happening. To find the odds in favor of an event, you can use the formula:

Odds in favor = probability of event occurring / (1 - probability of event occurring)

In this case, the event is that Adam will see a meteor in the next 10 minutes. The probability that this event will occur is 0.56. Therefore, the odds in favor of this event occurring are:

Odds in favor = 0.56 / (1 - 0.56)

= 0.56 / 0.44

= 1.27

So, the odds in favor of Adam seeing a meteor in the next 10 minutes are 1.27 to 1.

It means that Adam is 1.27 times more likely to see a meteor in the next 10 minutes than not seeing one.

Step-by-step explanation:

The odds in favor of Adam seeing a meteor in the next 10 minutes are 14 : 11

When we construct the confidence interval their sample must have some conditions which are as follows,

Therefore , these are the conditions which the administrator should use to construct a one-sample z interval for a proportion.

When two ratios are equivalent to each other , they are said to be in a state called proportion. The proportion formula is used to see whether  the given ratios or fractions are equal or not . The proportion formula can be given as, The product of means is equal to the the product of extremes. This can be written as ad = bc.

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y = 3x+4 ← equation of linear function.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have,

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = y_2-y_1/x_2-x_1

with (x₁, y₁ ) = (- 3, - 5) and (x₂, y₂ ) = (1, 7) ← 2 ordered pairs from the table

m = 7+5/1+3

  =12/4

   = 3 ,

So, y = 3x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (1, 7 ), we get,

7= 3 + c

⇒ c = 7-3

      = 4

Hence, y = 3x+4 ← equation of linear function

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You had a better score relative to the rest of your class.

To compare the scores of you and your friend relative to the rest of their classes, we need to calculate the standard deviation of your score and your friend's score from the average of their respective classes.

A standard deviation of 2 means that 68% of the scores in the class fall within 1 standard deviation of the mean, or between 84 and 88 in the case of Mrs. Wilson's class. Since 88 is greater than 86 (the mean) and less than 2 standard deviations away (88-86 < 2*2=4) , so your score of 88 is better than the average score in your class.

On the other hand, 85 is less than 82 (the mean) and more than 1 standard deviation away (85-82 > 2) so your friend's score of 85 is less than the average score in their class.

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On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).

Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]

Area = 1/2| 60 |

Area of pentagon  = 30 sq unit

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Answer:

15:18.75:26.25

Step-by-step explanation:

4:5:7

Total=16

60/16 = 3.75

4 x 3.75 = 15

5 x 3.75 = 18.75

7 x 3.75 = 26.25

15:18.75:26.25

Answer: $15 : $18.75 : $26.25

Step-by-step explanation:

4 + 5 + 7 = 16

4/16 × $60 = $15

5/16 × $60 = $18.75

7/16 × $60 = $26.25

Answer:

The two little blue boxes are going

Step-by-step explanation:

Lets start with the 0s.

Two zeros is 0. so its

_ _ _ _ 0.

Now we add 2 and 0 which is 2.

_ _ _ 2 0

now we add 6 and 4, which is 10. We have to put the 1 above the 7 and 5 and we are going to put 0 down below

_ _ 0 2 0

now we are going to add 7 +5, but dont forget the 1! Its going to be 13. Put the 3 down below and put the 1 above the 2!

_ 3 0 2 0

Now its 2 + 1 which is 3

your answer is

33020

By working together, they can make the work done in two hours and forty-six minutes.

Given data :

Think of these work rates as "greenhouses per hour", not "hours per greenhouse". Then Steve's work rate is one fourth of a greenhouse per hour, and his son's is one ninth of a greenhouse per hour. Now, multiply each rate by the time t to get the portion of the greenhouse each paints, and add the products up to get one greenhouse. The work equation becomes:

1 / 4 t + 1 / 9 t = 1

9 / 36 . t + 4 / 36 t = 1

13 / 36 t = 1

36 / 13. 13 / 36 t  = 36 / 13 .1

t = 36 / 13 hrs

or 36 / 13. 60 = 166 min

This is two hours and forty-six minutes.

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The x-coordinate of the centroid of the triangle ABC with vertices

A(-3, 3), B(2, 5), and C(4, -3) is 1.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

The centroid of a triangle is the common intersection point of all the medians of the triangle.

When vertices of a triangle is given the co-ordinate of the centroid are

(x₁ + x₂ + x₃)/3 and (y₁ + y₂ + y₃)/3.

Given, ΔABC has vertices A(-3, 3), B(2, 5), and C(4, -3).

Therefore, The x-coordinate of the centroid is,

Gₓ = (- 3 + 2 + 4)/3.

Gₓ = 3/3.

Gₓ = 1.

So, The x-coordinate of the centroid is 1.

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Answer:

31.25

Step-by-step explanation:

25% * 125 = 25/100 * 125 = 1/4 * 125 = 31.25

Following are three steps 1. Isolate the variable: First, identify the variable you are trying to solve for and use the other terms in the equation to isolate that variable. This means using inverse operations to move any terms containing the variable to one side of the equation and any terms without the variable to the other side of the equation.

2. Simplify the equation: Once the variable is isolated, use the properties of equality and inverse operations to simplify the equation, if needed.

3. Solve the equation: Finally, use the inverse operations to solve the equation and find the value of the variable.

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The probability that the sixth child will be a son is 50%. Each child, regardless of gender, has an equal chance of being born.

P(son) = (5 choose 6) x (0.5^6) = 0.015625

Therefore, the probability of having a son as the sixth child can be calculated using the binomial formula as follows: P(son) = (5 choose 6) x (0.5^6) = 0.015625.

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The population of a city is increasing at a rate of 4% each year. In 2020, there were. 236,000 people in the city.

Given, In 2015, the population of the town decreased by 10%, so [tex]8250 x 10/100 = 825[/tex]  people left the town, bringing the population down to [tex]8250 - 825 = 7425.[/tex]

From 2015 to 2020, the population increased by 15% so [tex]7425 x 15/100 = 1113.75[/tex] people came back to the town, bringing the population to [tex]7425+1113.75 = 8538.75[/tex]

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The number of hours of practice is 3 x h or 3h.

In mathematics, an expression is a sentence that contains at least one number or variable. Additionally, an expression consists of at least one mathematical operation. There is no equal to sign in an expression.

Given:

Volleyball practice is h hours long. Debbie had 3 volleyball practices last week.

Multiply the number of hours for each practice by the total number of practice to get the expression for the number of practice hours.

The mathematical operation known as multiplication is used to calculate the sum of two or more numbers.

Number of hours of practice

= hours of practice x number of practice

= 3 x h

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Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both.

For a square whose side are 2 units long is :

= 2 + 2 x 2 + 2

= ( 2 + 2 ) x 2

= 2 x 4

= 2 x 3 + 2 = 8

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Answer:

denominator - 6234 is math

Step-by-step explanation:

Therefore , the solution of the given problem of parallelogram comes out to be option D 80  degrees.

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Here,

Given : The parallelogram  has M angle  =100 degree

And to Find :L angle

In a parallelogram sum of the adjacent angle is 180°, So

So ,

Using this parallelogram property ,

we find :

=>100 + L =180

=> L = 80

Thus,

We get the L value using parallelogram properties.

Therefore , the solution of the given problem of parallelogram comes out to be option D 80  degrees.

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The inequality to find the cost of the pizza they should order is c ≤ 14. The cost is at most $14.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Trey and three of his friends are ordering a pizza and they want to spend at most $3.50 per person. An inequality to find the cost of the pizza they can order is:

c ≤ (3.50 × 4)

c ≤ 14

The cost will be at most $14.

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If the radius is quadrupled, then the area of the new area to the old area will be 4:1

You should be aware that the quadrupled of a circle is four times the area of the old one.

In this case the area of the circle is denoted by

Area = πr²

Where r= radius=6 cm

The area of the old circle is 22/7 * 6 * 6

Area of the circle is = 113.1cm²

To this effect, the area of the new circle is 4(area of the old one)

Area = 4*22/7 * 6 * 6

Area = 3167/7

Area is = 452.6

This implies that 4(113.2) =452.6

In conclusion, you will discover that four times the area of the new circle is the old circle

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The measure of the exterior angle of the triangle is 114 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The measure of the exterior angle of the triangle can be found using exterior angle theorem.

Therefore, the exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Hence,

24 + 2x + 18 = 3x + 6

2x - 3x = 6 - 18 - 24

-x = -36

divide both sides of the equation by -1

x = 36

Hence,

exterior angle = 3x + 6 = 3(36) + 6 = 108 + 6 = 114 degrees

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The solution for the rational equation (1/(x + 1)) - (1/(x + 2)) = 1/5 is specified by the option C.

C. x = -3.79, x = 0.79

A rational equation consists of a fraction that has a polynomial numerator denominator.

The specified equation can be expressed as follows;

[tex]\dfrac{1}{x + 1} - \dfrac{1}{x+2} = \dfrac{1}{5}[/tex]

Finding the common denominator for the right hand side expression, we get;

[tex]\dfrac{ (x + 2) - (x + 1)}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]

[tex]\dfrac{1}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]

[tex]\dfrac{1}{x^2+ 3\cdot x+ 2} = \dfrac{1}{5}[/tex]

Inverting both sides of the above equation, we get the following quadratic equation;

x² + 3·x + 2 = 5

x² + 3·x + 2 - 5 = 0

x² + 3·x - 3 = 0

The quadratic formula indicates that we get;

x = (-3 ± √(3² - 4×1×(-3))) ÷ (2 × 1)

x = (-3 + √(21)) ÷ 2 and x = (-3 - √(21)) ÷ 2

x ≈ 0.79 and x ≈ -3.79

The correct option is option C

C. x = -3.79, x = 0.79

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Answer:

Which ratio forms a probation with 18/30

=20/35

=50/90

=36/46

=60/100

Step-by-step explanation:

Answer:

[tex] \sf \: \frac{14}{3} [/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: \frac{7}{9} \times 6[/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{7}{9} \times 6[/tex]

[tex] \sf \rightarrow \: \frac{(7 \times 6)}{9} [/tex]

[tex] \sf \rightarrow \: \frac{42}{9} [/tex]

[tex] \sf \rightarrow \: \frac{14}{3} [/tex]

Hence, the product is 14/3.