A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 600 miles, for a total gas consumption of 35 gallons. How many gallons were consumed by each of the two cars that week?

The value of x in this problem, considering the intersecting chords, is given as follows:

x = 10.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Hence the value of x is obtained as follows:

12x = 15 x 8

12x = 120

x = 10.

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Hello there. To solve this question, we have to remember some properties about arithmetic sequences.

Given the first term of an arithmetic sequence and its common difference, we can determine the n-th term of the sequence using the following formula:

We know that a1 = 3 and d = 4, hence

Is the general formula for the n-th term of the sequence.

Plugging n = 22, we find

This is the 22nd term of this sequence.

this might help

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The probability of getting even number is 1/2.

It is a measure of happening or non-happening of outcomes of a random experiment.

P(E) = Number of favorable outcomes/Total number of outcomes

According to the given question

We have

A cube labeled 1 to 6

Therefore,

sample space = {1, 2, 3, 4, 5, 6}

⇒ Total number of outcomes = 6

Numbers of even number on a die = { 2, 4, 6}

⇒ Total number of favorable outcomes = 3

So, the probability of getting even number = \(\frac{3}{6} = \frac{1}{2}\)

Hence, the probability of getting even number is 1/2.

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Answer:

yes u are have a great day

Answer: 154 sq cm

Step-by-step explanation:

The value of the missing length to the nearest tenth are;

a. x = 7.5

b. x = 7.8

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Therefore ;

c² = a²+b²

a. x² = 9²-5²

x² = 81-25

x² = 56

x = √56

x = 7.5 ( nearest tenth)

b. using Pythagoras theorem also!

x² = 6²+5²

x² = 36+25

x² = 61

x = √61

x = 7.8( nearest tenth).

Therefore the value of the missing values are 7.5 and 7.8

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The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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The surface area of the triangular prism is B. 1,008 \(cm^{2}\)

Triangular Prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.

How to determine this

The surface area of the triangular prism =  Area of the front Triangle + Area of the triangle + Each sides of the triangle by the length of the triangular prism.

Area of the front and back triangle will be the the same given the same base and height

To find the area of the triangle = 1/2 * Base * Height

Where base = 12 cm

Height = 9 cm

Area = 1/2 * 12 cm * 9 cm

Area = 6 * 9 \(cm^{2}\)

Area of the one triangle = 54 \(cm^{2}\)

So, by multiplying each sides of the triangle by the length

= Base * Length

= 12 cm * 25 cm

= 300\(cm^{2}\)

Height * Length

= 9 cm * 25 cm

= 225 \(cm^{2}\)

Then, Hypotenuse * Length

= 15 cm * 25 cm

= 375 \(cm^{2}\)

Surface area = 54\(cm^{2}\) + 54\(cm^{2}\) * 300\(cm^{2}\) + 225\(cm^{2}\) + 375\(cm^{2}\)

Surface Area = 1,008\(cm^{2}\)

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Answer:

the second one makes more sense

Answer:

This question answer is defenetily answer B ( there is a slight association between hieght and weight)

Step-by-step explanation:

Because of how the number line is set up I do believe your answer will be B  Just remember the way the number line is set up when you put the number line there and how the dots of where the number line goes plays a huge part in finding your answers. :)

Hope this helps!!!!!!!!! :)

Answer:

18.9 is the correct answer

Answer:

yup your answer is correcto

Step-by-step explanation:

Answer:

Step-by-step explanation:

18 * 10 - 8 * 4    (remember pemdas)

180 - 32 =

148 cm²

Answer:

0.9703 = 97.03% probability that 15 or more of them would agree with the claim.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they agree with the claim, or they do not. The probability of an adult agreeing with the claim is independent of any other adult, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

75% of adults believe that an unattractive smile hurts career success.

This means that \(p = 0.75\)

Suppose that 25 adults are randomly selected.

This means that \(n = 25\)

What is the probability that 15 or more of them would agree with the claim?

This is:

\(P(X \geq 15) = 1 - P(X < 15)\)

In which:

\(P(X < 15) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 13) + P(X = 14)\)

14 is below the mean, so we start below and go until the probability is 0. Then

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 14) = C_{25,14}.(0.75)^{14}.(0.25)^{11} = 0.0189\)

\(P(X = 13) = C_{25,13}.(0.75)^{13}.(0.25)^{12} = 0.0074\)

\(P(X = 12) = C_{25,12}.(0.75)^{12}.(0.25)^{13} = 0.0025\)

\(P(X = 11) = C_{25,11}.(0.75)^{11}.(0.25)^{14} = 0.0007\)

\(P(X = 10) = C_{25,10}.(0.75)^{10}.(0.25)^{15} = 0.0002\)

\(P(X = 9) = C_{25,9}.(0.75)^{9}.(0.25)^{16} \approx 0\)

Then

\(P(X < 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0002 + 0.0007 + 0.0025 + 0.0074 + 0.0189 = 0.0297\)

And

\(P(X \geq 15) = 1 - P(X < 15) = 1 - 0.0297 = 0.9703\)

0.9703 = 97.03% probability that 15 or more of them would agree with the claim.

Answer:

\(\frac{2}{12}\) simplified to \(\frac{1}{6}\)

Step-by-step explanation:

4 = \(\frac{1}{12}\)

2 = \(\frac{1}{12}\)

\(\frac{1}{12}\) + \(\frac{1}{12}\) = \(\frac{2}{12}\) ÷ 2 = \(\frac{1}{6}\)

Answer:

6 Batches because if each batch calls for 1/3 of a cup of flour and you split 2 cups into 1/3 cups you would have 6 1/3 cups  

Step-by-step explanation:

Jordan can make 7.111 batches before 3 PM today.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Jordan uses a recipe to make yogurt putty.

He buys a bag of cornstarch containing 128 servings that are 1/8 cups each.

He needs \(2\frac{1}{4}\) cups for each batch of yogurt putty.

So, servings are 128 x (1/8)

= 16 cups.

To find the number of batches:

Use division,

16 / ( 9/4)

= 16 x 4/9

= 64 / 9

= 7.111

Therefore, 7.111 batches Jordan can make.

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Angie' s grandma drive 376 miles in each day.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The two cities are 752 travel miles apart.

And, It take 12 hours to drive that far.

Now,

Since, Angie' s grandma want to do the drive in two day.

So, The distance cover by Angie' s grandma in each day is,

= 752 / 2

= 376 miles

Thus, Angie' s grandma drive 376 miles in each day.

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a) All possible values of h are no solutions, as the equation \((h + 2)^2 + 1681 = 169\) has no real solutions.

b) The length of segment AB is 8 units, which is equal to the radius of circle C1.

c) Since there are no possible values of h, we cannot find the standard equations of the requested circles.

To solve the given problem, let's break it down into three parts:

a) Find all possible values of h:

The distance between the centers of circle C1 and C2 is given as 13 units.

The center of C1 is (-2, -40), and the center of C2 is (h, 1).

Using the distance formula, we can set up the equation:

\(\sqrt{[(h - (-2))^2 + (1 - (-40))^2]} = 13\)

Simplifying and solving for h:

\(\sqrt{[(h + 2)^2 + 41^2] } = 13\)

\((h + 2)^2 + 41^2 = 13^2\)

\((h + 2)^2 + 1681 = 169\)

\((h + 2)^2 = 169 - 1681\)

\((h + 2)^2 = -1512\)

Since the equation has no real solutions (a negative value under the square root), there are no possible values of h that satisfy the given conditions.

b) Find the length of segment AB:

Let A be the center of circle C1 (-2, -40), and B be the intersection of the segment connecting A and circle C1 with circle C2.

The radius of C1 is √64 = 8, and the radius of C2 is √81 = 9.

Since A is the center of C1 and AB is a radius, the length of segment AB is equal to the radius of C1, which is 8 units.

c) Find the standard equations of the circles concentric with C1 and tangent to C2 for each possible value of h:

Since there are no possible values of h (as determined in part a), we cannot find the standard equations of the requested circles.

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

x=3 and y=1

Step-by-step explanation:

First find the deteminant

That is ad-bc

ᵃ ᵇ

ᶜ ᵈ

The formula for the Child dependency ratio is,

Given:

Therefore,

Hence, the Child Dependency Ratio is

Answer:

Understgand what?

Step-by-step explanation:

Answer:

whats your question?

Step-by-step explanation:

Answer:

ABC is not a right triangle

Step-by-step explanation:

The angle ABC doesn't have a straight line. for one of the legs or sides. The angle is actually an acute angle. The angle ABD and DBC or right angles but I don't belive that ABC is a right angle

Answer: Yes,

Step-by-step explanation: ABC is a right triangle because angle B adds up to 90, to find angle B, we will need to find it first for the BDA and BDC triangle, we can do this using cos

for BDA cosθ  = 12/15

θ = cos^-1(12/15) = 36.86989765

for BDC cosθ = 12/20

θ = cos^-1(12/20) = 53.13010235

these two added together equal 90

Answer:

Step-by-step explanation:

2^3= 2 times 2 times 2=8

3^2= 3 times 3=9

(1/2)^3=1/2 times 1/2 times 1/2=1/8

Hope it helped! :)

Answer:

B, E

Step-by-step explanation:

A line has a negative slope when it decreases going left to right.

As the absolute value of the slope gets larger (-2 to -3 would be 2 to 3), the graph gets steeper (-3 is steeper than -2).

Answer:

B & E

Step-by-step explanation:

Ride block 1 has 4 hours and 30 minutes

Ride Block 2 has 5 hours and 30 mins

Answer:

  C:  y = -(x +3)² -1

Step-by-step explanation:

You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.

For vertex (h, k), the vertex form equation of a parabola is ...

  y = a(x -h)² +k

Given that (h, k) = (-3, -1), the equation will have the form ...

  y = a(x -(-3))² + (-1)

  y = a(x +3)² -1 . . . . . . . . . . matches choice C

The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.

  y = -(x +3)² -1

__

Additional comment

Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.

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Answer:

=0

Step-by-step explanation: