Find the sum. Give your answer as a
simplified mixed number

Answer:

x=10

Step-by-step explanation:

First, add 5 to both sides of the equation, getting rid of the -5 on the left side but still making them equal.

5x=3x+20

Then, do the same with 3x, Subtract from both sides.

2x=20

Lastly, Divide both sides by 2 and you'll get your answer

x=10

Answer:

[tex] \sf \: x = 10[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 5x - 5 = 3x + 15

Then the value of x will be,

→ 5x - 5 = 3x + 15

→ 5x - 3x = 15 + 5

→ 2x = 20

→ x = 20 ÷ 2

→ [ x = 10 ]

Hence, the value of x is 10.

Answer: x = y

Step-by-step explanation:

x and y are angles with vertical sides, and angles with vertical sides are always equal

Using the vertices given, the area of triangle PQR is 18 squared units

The area of triangle PQR can be found using the Shoelace Theorem. This theorem states that the area of a polygon can be calculated by taking the sum of the products of the coordinates of its vertices and subtracting the sum of the products of the coordinates of its vertices in reverse order.

In this case, the vertices of triangle PQR are P(-8, 2), Q(-2, 4), and R(-6, 8), so the area can be calculated as follows:

A = 1/2 * |(-8 * 4) + (-2 * 8) + (-6 * 2) - (2 * -2) - (4 * -6) - (8 * -8)| = 1/2 * |-32 + 16 + -12 - 4 + 24 + 64| = 1/2 * |36| = 18 square units

So the area of triangle PQR is 18 square units.

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We can use the sine ratio to solve this problem and the value of x would be 8.604.

What are trigonometric ratios?

Trigonometric ratios are ratios of the side lengths of a right triangle with respect to its acute angles.

Sine (sin) ratio: The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In the given figure, we have given the hypotenuse of the triangle, and  an angle is given which is opposite to 35 degree, so we can use the sine ratio to find the value of x

sin35°= x/15

To solve for x, we can use the following steps:

Multiply both sides of the equation by 15 to isolate x:

sin 35° = x/15

15 * sin 35° = x

Use a calculator to approximate sin 35°:

sin 35° ≈ 0.5736

Substitute the approximation into the equation and solve for x:

x = 15 * 0.5736

x ≈ 8.604

Therefore, x is approximately equal to 8.604.

Hence, we can use the sine ratio to solve this problem and the value of x would be 8.604.

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Answer:

The correct answer is C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles.

This statement uses the definition of supplementary angles, which states that two angles are supplementary if their measures add up to 180 degrees. Since ∠3 and ∠6 are corresponding angles, and ∠4 and ∠5 are also corresponding angles, their measures must add up to 180 degrees in order for the parallel lines to be cut by the transversal.

Answer:

Option, D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem

Step-by-step explanation:

In this question that you have put:

7 ≅ ∠6 and ∠8 ≅ ∠5 Reason =

Vertical Angles Theorem ( Or in similar terms VAT )

Make sure that you remember the following:

vertical angles are the angles that are opposite each other when the two line " meet together "

Thus, your answer to your questions is.

D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem

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1) The probability of picking more than 1 apple is 0.8. 2) the expected number of apples you can pick each year is 2.65. 3) the expected number of apples you can pick each year is 2.65.

To find the probability of picking more than 1 apple, we need to find the sum of the probabilities of picking 2, 3, and 4 apples. Using the table, we have P(N>1) = P(2) + P(3) + P(4) = 0.15 + 0.35 + 0.3 = 0.8. So, the probability of picking more than 1 apple is 0.8. The expected number of apples you can pick each year can be calculated using the formula: E(N) = ∑N * P(N), where the sum is taken over all possible values of N. Using the table, we have E(N) = (1 * 0.1) + (2 * 0.15) + (3 * 0.35) + (4 * 0.3) = 0.1 + 0.3 + 1.05 + 1.2 = 2.65. So, the expected number of apples you can pick each year is 2.65. To find the probability of picking 3 apples, given that your father picked more than 1 apple, we need to use the conditional probability formula. We have P(3|N>1) = P(3 and N>1) / P(N>1) = P(3) / P(N>1) = 0.35 / 0.8 = 0.4375. So, the probability of your father picking 3 apples, given that he picked more than 1 apple, is 0.4375

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Complete Question

Imagine you have an apple tree, and you pick apples from it each fall. Empirically, the number of apples (N) that you can harvest and the corresponding probability (P) can be summarized in the following table,  the table =  N - O, 1, 2, 3, 4 And P = 0.1, 0.15, 0.35, 0.3, 0.1

1) What is the probability that you can pick more than 1 apple? 2) What is the expected number of apples you can pick each year? 3) Your father told you that he picked more than 1 apple this year. What is the probability that he picked 3 apples, given that information?

The obtuse angle such that has the same sine as -275° is θ = 95°

We want to find an obtuse angle (with a measure larger than 90°) in the range 0 ≤ θ ≤ 2π (or 0 < θ < 360°, after that we can change the units from degrees to radians) such that sin(θ) = sin(-275°)

First, remember that the sine function has a periodicity of 360°, then:

sin(-275°) = sin(-275° + 360°) = sin(85°)

Now we know that the sine function is symmetric around x = 90°

Then:

sin(90° + x) = sin(90° - x)

if we take x = 5° we will get:

sin(90° + 5°) = sin(90° - 5°)

sin(95°) = sin(85°) = sin(-275°)

Thus we can conclude that θ = 95°

That is the obtuse angle.

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The simplified form of the numerical expression  (9² - 4 - 4) - (- 2³ - + 12) is 93.

Numerical expression is a combination of the words numerical, which refers to numbers, and expression, which denotes a statement. Consequently, it is a statement that uses numbers.

Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.

By mixing numbers with different mathematical operators, we can create a numerical expression. There is no restriction on how many operators can be used in a numerical expression. Between two numbers, some mathematical expressions utilize just one operator, whereas others may use multiple operators.

Given, An expression (9² - 4 - 4) - (- 2³ - + 12).

= (9×9 - 8) - (- 2×2×2 - 12).

= (81 - 8) - (- 8 - 12).

= (73) - (- 20).

= 73 + 20.

= 93.

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The sketch of the front elevation and the side elevation of the prism are added as an attachment

From the question, we have the following parameters that can be used in our computation:

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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The probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants is 0.9941.

The probability distribution of x, where x is the number of seeds that grow into healthy plants when 75 seeds are planted, is a binomial distribution with parameters n = 75 and p = 0.69. The probability of x = 44 is calculated by using the formula for the probability mass function of the binomial distribution:

[tex]P(x=44) = (75 choose 44) * (0.69)^44 * (1-0.69)^(75-44) = 0.1578[/tex]

The probability of x >= 44 is calculated by using the formula for the cumulative probability function of the binomial distribution:

[tex]P(x > = 44) = 1 - P(x < = 43) = 1 - (75 choose 43) * (0.69)^43 * (1-0.69)^(75-43) = 0.7406[/tex]

The probability of x > 44 is calculated by subtracting the probability of x = 44 from the probability of x >= 44:

P(x > 44) = P(x >= 44) - P(x = 44) = 0.7406 - 0.1578 = 0.5828

The probability of 19 <= x <= 53 is calculated by subtracting the probability of x <= 18 from the probability of x <= 53:

[tex]P(19 < =x < =53) = P(x < =53) - P(x < =18) = 0.9994 - 0.0053 = 0.9941[/tex]

Therefore, the probability that exactly 44 seeds grow into healthy plants is 0.1578, the probability that at least 44 seeds grow into healthy plants is 0.7406, the probability that more than 44 seeds grow into healthy plants is 0.5828, and the probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants is 0.9941.

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Answer: Is only definable if you can show the table but according to a valid explanation it would be most likely 41

Step-by-step explanation:

Lets say Bob has 17 strawberry, 19 Cola, and 4 blueberry, we can infer there is an equal amount of gumballs of each flavor in the machine; Before bob bought any gumballs there were 180 and if there were only 3 flavors we would divide 180 by 3 and get 60. That means each flavor has 60 of its own flavor and if we take 19 from the 60 cola flavored we can get 41.

Answer: 0.342 -> 0.394 -> 0.439 -> 0.441 -> 0.531

Step-by-step explanation:

0.342 -> 0.394 -> 0.439 -> 0.441 -> 0.531

If you convert the decimals into fractions out of a hundred, then it will be easily to keep going from least to greatest or greatest to least and soon you won't need help. Keep trying! :)

The expected value of the policy for the insurance company: $359.38

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The expected value of the policy for the insurance company can be calculated as follows:

Expected value = (Probability of survival) x (Annual payment)

= 0.999057 x $360

= $359.38

So, the expected value of the policy for the insurance company is $359.38.

It's important to note that this is just an estimate based on statistical probabilities and does not guarantee the outcome. The actual value could be higher or lower than this estimate, depending on the actual lifespan of the policyholder.

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The missing term in the equation is n = -2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the missing term be represented as n

-2x + 18 = nx + 18

Subtracting 18 on both sides of the equation , we get

-2x = nx

Divide by x on both sides of the equation , we get

n = -2

Therefore , the missing term is n = -2

Hence , the equation is n = -2

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Answer: j = -8

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

2j = 16 + 4j

collecting like terms, you would have

2j - 4j = 16

-2j = 16

divide both sides by 2

j = 16/(-2)

j = -8

The ratio tables based on the information will be:

12 16

3 4

36 48

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

This simply indicates that you're dividing the variable A by B. Let us say for instance, the ratio will be 3/10 if A is 3 and B is 10.

Since the ratio is 3:4. When the smaller number is 36, the larger number will be:

= 4/3 × 36.

= 48

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The 7 metric units are part of the International System of Units, and this are km, m, cm, mm, kg, g and L. Each unit is based on a multiple of 10, making it easy to convert between them.  For example, 1 kilometer is equal to 1000 meters, and 1 kilogram is equal to 1000 grams.

The 7 metric units are as follows:

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Todd has done correct calculation its values is equal to 6.79, which is closer to 7.

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number on the top side, it indicates the number of equal parts taken or whole quantity and denominator is on the bottom side, it indicates the equal parts of the whole quantity.

Given that,

Two fraction numbers in the form of addition,

⇒ 3 7/8 + 2 11/12

It can be further solved as

⇒  (24 + 7)/8 + (24 +11)/12

⇒  31/8 + 35/12

Now taking LCM of (8, 12)

LCM(8, 12) = 24

making denominator same in the both terms

⇒ 93/24 + 70/24

⇒ 163/24

⇒ 6.79

Thus, the values is closer to 7

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The Solution using two methods are 323, .291, the correct option is B`.

Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.

Given;

Frank is a champion fish charmer who can charm fish with .62 probability of success

He attempts to charm 100 fish, what's the probability he'll charm

between 60 and 80 inclusive

Now, probability out of 100

=62

This is between 60 and 80

So, 323

Therefore, the probability will be 323 and .291

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Answer: A, B, F

Step-by-step explanation:

For convenience sake, let's establish early on that 1/2 is equal to 0.5 or 50% in their decimal and percentage forms respectively.

- A as a decimal is 0.25, which is not only smaller than 1/2, but it is exactly half of the value, so A works.

- B is also smaller than the decimal of 0.5, therefore it counts.

- 3/5 as a decimal is 0.5, which is greater, so doesn't count.

- 67% is bigger than 50%, so doesn't count.

- 0.74 is bigger than 0.5, so doesn't count.

- 40% is smaller than 50%, so it counts.

Answer:

A, B, and F

Step-by-step explanation:

A. 1/4 = 25%

B. .26 = 26%

F. 40%

The value of z   is -1.09.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data collection.

Given: P(Z<z)=0.14

To find the value of z such that 0.14 of the area lies to the left of z.

We will use z-score table to get the value of z here.

IN z-score table, we have

For P(Z<-1.09)=0.14

Hence, the value of z is -1.09.

Its approximate value is -1.09

So the final answer is z=-1.09.

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The area of the walkway of the garden is  8x - 15 square units.

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

Given, The area of the garden is 2(3.5x + 2.5) and the combined area of the garden and the walkway is 2.5(6x + 4).

Therefore, The area of the walkway is,

= 2.5(6x + 4) - 2(3.5x + 2.5).

= 15x - 10 - 7x - 5.

= 15x - 7x - 10 - 5.

= 8x - 15 square units.

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James runs 400m in a day

In a week = 7 days

400m × 7 days = 2800m

To convert 2800m to km

1km = 1000m

So, 2800m/1000m

= 2.8 km

How far are the Town Center and the Park

3.5 km and 650m

650m to km

1km = 1000m

To km  = 0.65km

The distance = 3.5km - 0.65km

= 2.85km

So, they are 2.85km apart

A bottle  = 1.75 liters of lemonade

A can = 330 ml of lemonade

1.75 liters to milliliters

1 liter = 1000 milliliter

= 1.75 × 1000 ml

= 1750 ml

2 bottles of lemonade

1750ml × 2

= 3500 ml

6 cans of lemonade

330ml × 6

= 1980 ml

In total, 3500ml + 1980ml

= 5480 ml

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The area of the given triangle is 28 squared feet

The area of a triangle is a measure of the amount of space enclosed by the triangle. It is a scalar quantity, meaning that it is a single numerical value with no direction.

The area of a triangle can be calculated using various formulas, depending on the information available about the triangle.

In this problem, we have the value of base and the height of the triangle.

The formula is given as;

A = 1/2 b * h

Substituting the values into the formula;

A = 0.5 * 7 * 8

A = 28 squared feet

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Answer:

About 54 geckos

Dividing with an area model and multiplying with an area model are similar in that they both involve partitioning a rectangular area into smaller parts.

However, dividing with an area model involves starting with the total area and then dividing it into equal parts to find the size of each part. For example, to divide 12 by 3, we could draw a rectangle with an area of 12 and then partition it into 3 equal parts to find that each part has an area of 4.

Multiplying with an area model involves starting with the size of the smaller parts and then combining them to find the total area. For example, to multiply 3 by 4, we could draw a rectangle with a width of 3 and a height of 4 and then calculate the area of the rectangle as 12.

So, while both methods involve using an area model, dividing starts with the total area and finds the size of the parts, while multiplying starts with the size of the parts and finds the total area.

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The value of the house when it was purchased was $150,000, before the 38% discount was applied.

A discount is a reduction in price or value, typically given as an incentive to purchase or to compensate for a decline in value.

In this case, we know that the house has decreased in value by 38% since it was purchased. This means that the current value is only 62% of its original value (100% - 38% = 62%).

Now, we can use a proportion to determine the original value of the house. We can set up the equation:

Current value / Original value = 62% / 100%

Substituting the given values, we get:

$93,000 / Original value = 62 / 100

To solve for the original value, we can cross-multiply and simplify:

100 x $93,000 = 62 x Original value

$9,300,000 = 62 x Original value

Dividing both sides by 62, we get:

Original value = $150,000

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