Match the number in scientific notation to the same number in standard notation.

The statement "It is valid because Victoria added the same amount to each side of the equation" correctly explains whether equation 3 in Victoria's work is valid in solving the equation.

In equation 3, Victoria added 3 to both sides of the equation x-3=4/21. This operation is valid because she added the same amount (3) to both sides, which maintains the equality between the two sides of the equation. The resulting equation is x-3+3=4/21+3, which simplifies to x=4/21+63/21 or x=67/21.

Therefore, equation 3 is a valid step in solving the equation x-3=4/21.

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Answer: y = -15/14x - 1/2

Step-by-step explanation:

Start:

15x + 14y = -7

Subtract 15x from each side:

14y = -15x - 7

Divide 14 on each side:

y = -15/14x - 1/2

If you want to simplify the slope, it would be:

y = -1 1/14x - 1/2

Hope this helps!

A group of 10 people would raise a total value of  $160 if they worked 16 hours.

According to the given information, the amount of money raised, R, varies jointly as the square root of hours worked, h, and the number of people working, p. This means that R = k√h * p, where k is the constant of proportionality.

We are given that six people raise $72 when working 9 hours, so we can use this information to find the value of k:
72 = k√9 * 6
72 = k * 3 * 6
72 = 18k
k = 4

Now that we know the value of k, we can use it to find the amount of money that 10 people would raise if they worked 16 hours:
R = k√h * p
R = 4√16 * 10
R = 4 * 4 * 10
R = 160

Therefore, 10 people would raise $160 if they worked 16 hours.

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Answer:

180 p

Step-by-step explanation:your welcome

The given histogram is right skewed type.

A histogram is a graphic representation of data in a grouped frequency distribution with continuous classes.

They are similar to a bar graphs, but there are no gaps between the consecutive rectangles.

Histograms are widely used for ranging data into groups. It is a highly practical graph due to its clarity and simplicity.

Histogram :-

It is a collection of rectangles next to one another, where each bar represents a different type of data.

In this context, frequency refers to the number of times a number appears in statistical data.

It is known as a frequency distribution when shown in a table.

Here, the distribution here is skewed to the left. Therefore, it is also referred to as a negatively skewed histogram graph.

Hence, the given histogram is right skewed type.

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A middle school basketball player makes a free throw with a probability of 0.6. Assuming each free throw is an independent event,the probability the player makes zero of their next three free throws is  0.064. The correct answer is A.

The probability that a middle school basketball player makes zero of their next three free throws can be calculated using the formula P(A) = P(A')ⁿ, where P(A) is the probability of the event occurring, P(A') is the probability of the event not occurring, and n is the number of trials.

In this case, P(A) is the probability of the player making zero free throws, P(A') is the probability of the player missing a free throw (1 - 0.6 = 0.4), and n is the number of free throws (3).

Using the formula, we can calculate the probability of the player making zero free throws as follows:

P(A) = P(A')ⁿ
P(A) = (0.4)³
P(A) = 0.064

Therefore, the correct answer is (A) 0.064.

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Answer: 5.25

Step-by-step explanation:

In the picture there is a smaller triangle inside a bigger triangle. You have to find the size it grows by dividing a side of the bigger triangle to the same side of the smaller triangle.

16.8/6.4 = 2.625

Then you find x by multiplying the adjacent side by the size it grows.

2*2.626 = x

2*2.626 = 5.25

Answer:

17,000

Step-by-step explanation:

17000 in words is written as Seventeen-thousand. The number 17000 represents a value equivalent to it.

Answer:

720

Step-by-step explanation:

The number of permutations of the letters of the word MAKABAYAN is 720. This is because the word MAKABAYAN has 9 letters, and the formula for calculating the number of permutations of a word with n letters is n! (n factorial). Therefore, 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 720

The solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].

To solve the inequality 2r - 5 ≤ 9, we need to isolate the variable r on one side of the inequality. Here are the steps to do so:

Now, we can present our answer in interval notation. Interval notation is a way to represent an interval on the number line. It is written in the form of [a, b], where a and b are the endpoints of the interval. The square brackets mean that the endpoints are included in the interval.

Since our inequality is r ≤ 7, our interval notation would be (-∞, 7], where -∞ represents negative infinity and 7 is the endpoint. The square bracket on the 7 means that 7 is included in the interval.

Therefore, the solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].

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An expression that shows the total area of five rooms is (3 × 13²) + (2 × 15²)

The correct answer is an option (A)

Let 'a' represents the side length of the square rooms measuring 13 ft each and 'b' represents the side length of the square rooms measuring 15 ft each.

We know that the formula for the area of a square  is A = s²

where 's' is the side of a square.

Sides of three square rooms measure 13 feet each.

So, the area of the three rooms would be:

A₁ = 3 × a²

A₁ = 3 × 13²

And sides of two square rooms measure 15 feet each.,

So, the area of the two rooms would be:

A₂ = 2 × b²

A₂ = 2 × 15²

Total area of the five rooms A =  A₁ + A₂  

So, we get an expression:

A = 3 × 13²  + 2 × 15²

A = 3 × 169 + 2 × 225

A = 957 ft²

Therefore the total area of the five rooms be 957 ft².

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The complete question is:

Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms?

a.(3 × 13^2) + (2 × 15^2)

b.(2 × 13^3) + (2 × 15^2)

c.(3 × 15^2) + (2 × 13^2)

d.(3 × 13^2) × (2 × 15^2)

Answer:

see below

Step-by-step explanation:

put paragraph of words into summarised information 1st.

ie

black : red : total

7 : 2 : 7+2 = 9 is total units

total units = 9 (which is 144 markers)

so 1 unit is .....

144 ÷ 9 = 16 markers

black = 7units

7 x 16 markers = ans

red = 2 units

2 x 16 = ans

Javier has 90 more uncommon cards than rare cards.

To find out how many more uncommon cards Javier has than rare cards, we need to multiply the number of packs he has by the number of each type of card in a pack, and then subtract the number of rare cards from the number of uncommon cards. We can do this with the following equation:

Uncommon cards - Rare cards = Difference

First, we'll multiply the number of packs by the number of each type of card:

45 packs × 3 uncommon cards = 135 uncommon cards
45 packs × 1 rare card = 45 rare cards

Now we'll subtract the number of rare cards from the number of uncommon cards to find the difference:

135 uncommon cards - 45 rare cards = 90

So, the number of uncommon cards is 90 more than the rare cards.

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The measure of the central angle indicated is 60°.

The central angle of a circle is the angle that an arc takes up in the centre. The radius vectors are what make up the angle's arms.

The formula for calculating a central angle is: Central Angle = Arc length (AB) / Radius (OA) = (s 360°) / 2r, where "s" stands for arc length and "r" for circle radius.

Now here in the given diagram,

Let x equal the desired angle.

The central angle that we need to find is:

Now x = 360-120-(90+90)

⇒ x = 360-300

⇒ x = 60°

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(a) The possible number of positive real zeros of P(x) can be determined using Descartes' Rule of Signs. The Rule of Signs states that a polynomial with real coefficients can have at most as many positive real zeros as its leading coefficient has sign changes in the coefficients. This means that the polynomial has at most 3 positive real zeros.

(b) Descartes' rule of signs can also be used to prove that 1-2 cannot be a zero of P(x). According to the Rule of Signs, the number of positive real zeros of P(x) is limited to 3. However, if 1-2 is a zero of P(x), then the polynomial would have 4 sign changes, which is not possible. Therefore, 1-2 cannot be a zero of P(x).

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Answer:

I think its 560

Step-by-step explanation:

The formula for standard error of proportion is √(pq/n) where p is the sample proportion, q = 1-p, and n is the sample size. Here, the sample proportion is 0.75, q is 0.25, and n is 160. Therefore, the standard error of proportion is √(0.75*0.25/160) = 0.035

The probability that between 120 and 128 patents (inclusive) are friends with their children can be calculated using the z-score formula:
z = (x - np)/√(npq)
where x is the number of parents between 120 and 128 who are friends with their children,
np = 160*0.75 = 120, and pq = 160*0.25 = 40.
Therefore,√(npq) = √(120*40) = 24.49
z = (120 - 120)/24.49 = 0
z = (121 - 120)/24.49 = 0.04
z = (122 - 120)/24.49 = 0.08
z = (123 - 120)/24.49 = 0.12
z = (124 - 120)/24.49 = 0.16
z = (125 - 120)/24.49 = 0.2
z = (126 - 120)/24.49 = 0.24
z = (127 - 120)/24.49 = 0.29
z = (128 - 120)/24.49 = 0.33

Using a z-table or a calculator, the probability that z is between 0 and 0.33 is 0.1292. Therefore, the probability that between 120 and 128 parents are friends with their children is 0.1292.

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It seems like the question is asking about a system of equations with no restrictions on the variables b1, b2, and b3. However, the question is filled with typos and formatting errors that make it difficult to understand the exact problem and provide an accurate answer. It would be best to ask the student to clarify the question and provide a properly formatted version of the problem before attempting to answer.

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Answer: Using the given functions, we can model the distance, d(t), that the car is from the city as:

d(t) = f(t) + g(t) = 10 + 65t

So, after 2 hours of driving, the distance that the car has traveled from the city is:

d(2) = 10 + 65(2) = 10 + 130 = 140 miles

Therefore, Riordan is incorrect, and the correct distance the car is from the city after 2 hours of driving is 140 miles.

Step-by-step explanation:

An expression to represent the total amount of juice left in the jar is "Total amount of juice left in jar = Total amount of juice in jar before Celina drinks any - Amount of juice Celina drinks"

First, let's start by labeling the quantities of juice we have. We have 0.85 liters of strawberry juice, 0.50 liters of mango juice, and 0.15 liters of watermelon juice. When we combine these three quantities, we get the total amount of juice in the jar before Celina drinks any of it. We can express this as:

Total amount of juice in jar before Celina drinks any = 0.85 + 0.50 + 0.15

Simplifying this expression, we get:

Total amount of juice in jar before Celina drinks any = 1.50 liters

Now, we know that Celina drinks 0.30 liters of the mixture. So, the total amount of juice left in the jar after she drinks some can be expressed as:

Total amount of juice left in jar = Total amount of juice in jar before Celina drinks any - Amount of juice Celina drinks

Substituting in our values, we get:

Total amount of juice left in jar = 1.50 - 0.30

Simplifying this expression, we get:

Total amount of juice left in jar = 1.20 liters

Therefore, the expression that represents the total amount of juice left in the jar after Celina drinks 0.30 liters of the mixture is:

Total amount of juice left in jar = 1.50 - 0.30 = 1.20 liters

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Complete Question:

A jar contains 0.85 liter of strawberry juice and 0.50 liter of mango juice. Celina poured 0.15 liter of watermelon juice into the jar. She then drank 0.30 liter of the mixture.

Part A: Write an expression to represent the total amount of juice left in the jar.

Answer:

C

Step-by-step explanation:

The equation that shows the whole amount of pizza Miah ate on Saturday is 3/32 of the whole pizza

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem are interpreted to mathematical equation

The left over is calculated is 3/8

therefore 5/8 of the pizza is left for Saturday

On Saturday she ate 1/4 of the pizza

= 1/4 × 3/8

= 3/32

therefore Miah ate 3/32 of the whole pizza on Saturday.

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Answer: C, 2 2/8

Step-by-step explanation: To turn a mixed number into an improper fraction, multiply the whole number by the denominator. Then, add the numerator. So in this example it would be:

4 3/8 = 35/8

2 1/8 = 17/8

Now, since the denominators are equivalent, all we need to do is subtract the numerators.

35/8 - 17/8 = 18/8

The answer needs to be changed back to a mixed number. For this problem, there is an easy way to do this.

18/8 = 8/8 + 8/8 +2/8, which as a mixed number would be 2 2/8.

So the correct choice would be (C).

In the quadrilateral ABCD if AB ||CD and  AB=9 as well as are CD=9. Then, quadrilateral ABCD is both parallelogram and trapezium.

Parallelogram's characteristics

In the quadrilateral ABCD:

Thus, the quadrilateral ABCD is both parallelogram and trapezium.

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Answer:

Step-by-step explanation:

For this triangle, we can find the angle adjacent to side length 4 using trig:

tan(theta) = 7/4

theta = tan^-1(7/4)

theta = 60.26

Now we use sine to find x:

sin(60.26) = 7/x

x = 7/sin(60.26)

x = 8.06

I don't know how far you need to round, so it can either be this or 8.1

Hope this helps!

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\pi (3)^2(4)\implies \stackrel{ \pi =3.14 }{V=113.04}[/tex]

The required solutions are as follows,
(a) The parabola will open downwards and have a maximum.
(b) The axis of symmetry for this function is t = 15.

A parabola is a cross-section cut out of the cone and represented by an equation shown in the question.

Here,
(a) The function C(t) is a quadratic function with a coefficient of -0.2 in front of the t² term. Since this coefficient is negative, the parabola will open downwards and have a maximum.

(b) The axis of symmetry of a quadratic function in the form of f(x) = ax² + bx + c is given by the formula x = -b/2a.

In this case, the function is C(t) = -0.2t² + 6t + 28.5, so a = -0.2 and b = 6. Thus, the axis of symmetry is:

t = -b/2a = -6/(2*(-0.2)) = 15

Therefore, the axis of symmetry for this function is t = 15.

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The properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms ln(√z) = (1/2)ln(z)

What is the logarithms?

Logarithms are mathematical functions that help to solve exponential equations. They are used to express very large or very small numbers in a more convenient and manageable way.

We can use the property of logarithms that states:

logb (a∙c) = logb a + logb c

to expand the expression as a sum of logarithms:

ln(√z) = ln(z^(1/2))

Using the power rule of logarithms, we can simplify this as:

ln(z^(1/2)) = (1/2)ln(z)

Hence, we can write:

ln(√z) = (1/2)ln(z)

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