Which situation can be represented by the expression 3 + (−7)?
A. A football team lost 3 yards on one play. The team gained 7 yards on the next play.
B. A football team gained 3 yards on one play. The team lost 7 yards on the next play.
C. A football team gained 3 yards on one play. The team gained 7 yards on the next play.

Picture 1: w = 14 units

Picture 2: The angles are 30°, 60° and 90°

Picture 3: p = 22√2 units

Picture 4: The distance is 42 ft

Picture 5: The perimeter of the equilateral triangle is 30√3 m

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

Picture 1

cos 30° = 7√3 / w

w cos 30° = 7√3

w  = 7√3 /(cos 30°)

w = 14 units

Picture 2

We have a right angle there already i.e. 90°. Let the two unknown angles be x and y.

sin x = (7√3) /(14√3)

sin x = 1/2

x = arcsin (1/2)

x = 30°

y = 90 - 30 = 60°

Thus, the angles are 30°, 60° and 90°

Picture 3

sin 45° = p/44

p = 44 * sin 45°

p = 44 * (√2)/2

p = 22√2 units

Picture 4

The distance from corner to corner is the length of the diagonal of the square.

Distance = √(30² + 30²) = 42 ft    (Pythagoras' theorem)

Picture 5

The perimeter of the equilateral triangle is the sum of all three sides.

Let's find the side x:

sin 60° = 15/x

x = 15/sin 60°

x = 10√3 m

perimeter = 3x = 3 * 10√3 = 30√3 m

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Answer: 27 masks

Step-by-step explanation:   2/3 = 1 mask

1 yard = 3/2

18 yards=3/2 * 18 = 27 masks

Hello! your answer is:

6 miles per hour

explanation:

Distance traveled, d = 2 1/2 miles = 5 / 2 miles

time taken, t = 5 / 12 hour

Speed is defined as the ratio of distance traveled to the time taken.

speed = 6 miles per hour

Thus, the unit rate of Chen is 6 miles per hour.

The probability that it rains today= 0.08

The probability that it doesn't rain todays= 0.16

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Given:

probability that it rains in London on any particular day is 0.4.

probability of it raining the following day decreases to 0.25.

For next two days

The probability that it rains today= 0.2 * 0.4 = 0.08

The probability that it doesn't rain todays= 0.4*0.4 = 0.16

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Answer:

(3,-19)

Step-by-step explanation:

To find the approximation where both functions equal, find where both lines intersect at. Both lines intersect in the Fourth Quadrant so The first 2 are wrong.

The y coordinate is lesser than -10 so the 4th one is wrong.

The answer is (3,-19)

Explanation:

The solution to f(x) = g(x) is where the f(x) and g(x) curves cross, aka the intersection point.

Based on the graph alone, it's a bit tricky to tell where they cross. Luckily, your teacher gave you multiple choices to pick from. We can rule out choices A and B since x < 0 here, but the x coordinate of the intersection is positive.

Choice D can be ruled out because the intersection point has a y coordinate such that -20 < y < -15. It looks like y is much closer to -20 than it is to -10. So there's no way to have y = -8 happen.

The only thing left is choice C. It appears that the intersection point could be (3,-19).

The measure of angle BCA is 81 degrees.                                            

Answer:

1. congruent? No

Similar? Yes

2. congruent? No

similar? yes

3. congruent? no

similar? yes

4. congruent? yes

similar? yes

I tried my best I hope it's right

16) Yes because each probability is between 0 and 1 and sum of all probability equals 1 so option A . 17) (D)= 0.44  18)(C)=1.7            
    
A) yes because each probability is between 0 and 1 and sum of all probability equals 1.            

:   ( σ <p(x)<1 and  Σ p(x)=1)

17)  probability that random selected passenger car an highway contain 2 or more people is 0.44

(P(x≥ 2)=p(x=2)+p(x=3)+p(x=4)+p(x=5)
P(x≥ 2=0.44
OR P(x≥ 2)=1-p(x≥ 2)=1-p(x=1)=1-0.56
p(x≥ 2)=0.44

18) Mean number of people in passenger cars are

E(X)=Σxp(x)=(1*0.56)+(2*0.28)+(3*0.08)+(4*0.06)+(5*0.02)
E(X)=1.7                        


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Answer:

Diameter Length: ( About ) 5.4 km; Option B

Step-by-step explanation:

~ Let us apply the Area of the Circle formula πr^2, where r ⇒ radius of the circle ~

1. We are given that the area of the circle is 22.9 km^2, so let us substitute that value into the area of the circle formula, solving for r ( radius ) ⇒ 22.9 = π * r^2 ⇒ r^2 = 22.9/π ⇒ r^2 = 7.28929639361.... ⇒

radius = ( About ) 2.7

2. The diameter would thus be 2 times that of the radius by definition, and thus is: 2.7 * 2 ⇒ ( About ) 5.4 km

Diameter Length: ( About ) 5.4 km

Answer:

a

Step-by-step explanation:

Answer:

233

Step-by-step explanation:

932 / 4 = 233

When conducting an assessment, the nurse observes fine, downy hair covering the newborn's shoulders and back. This finding is interpreted as lanugo.

So, the correct answer is B.

Lanugo is a soft, fine hair that covers the fetus and sometimes remains on the newborn's body after birth, particularly in preterm infants.

Milia are small, white bumps on a baby's skin, while vernix caseosa is a white, waxy substance that protects the baby's skin in the womb. Harlequin sign is a temporary skin color change in newborns. In this case, lanugo is the appropriate term to describe the observed hair on the baby's shoulders and back

Hence, the answer of the question is B.

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Two samples can have the same mean but different standard deviations due to the spread of data around the mean. Standard deviation is a measure of how much the data values differ from the mean. The greater the deviation of the data points from the mean, the greater the standard deviation.

Two samples can have the same mean but different standard deviations because standard deviation is a measure of the spread of data around the mean. If the data values are tightly clustered around the mean, the standard deviation will be small. If the data values are spread out around the mean, the standard deviation will be large. Therefore, two samples can have the same mean but different standard deviations because the spread of data around the mean can be different for each sample.

Two samples can have the same mean but different standard deviations because the spread of data around the mean can be different for each sample. For example, consider two samples of test scores. Sample A has a mean score of 80 and a standard deviation of 5. Sample B has a mean score of 80 and a standard deviation of 10. The scores in Sample B have more variability than the scores in Sample A.In a bar graph, the means of the two samples can be represented by two bars with the same height. The standard deviations of the two samples can be represented by error bars on each bar. The error bars show the variability of the data in each sample. The length of the error bars for Sample B would be longer than the length of the error bars for Sample A.

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The triangles ΔGFN and ΔJFN are congruent to each other by the SAS postulate. Then ∠FGN = ∠FJN.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The line segment GF = NJ and FN bisect the angle ∠GFJ.

In triangles ΔGFN and ΔJFN, then we have

GF = NJ                        (Given)

∠GFN = ∠JFN              (Given)

NF = NF                        (Common sides)

The triangles ΔGFN and ΔJFN are congruent to each other by the SAS postulate. Then we have

∠FGN = ∠FJN

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Answer:

15, 16, an 17.

Step-by-step explanation:

at most 12, meaning it can't be more but can be equal or less than that number.

18-5≠x-5≤12

17-5=x-5≤12

16-5=x-5≤12

15-5=x-5≤12

Answer:

the simplest form is ⅓...............

The dimensions of the rectangular enclosure for his garden is length of 8.0 m and width of 8.0 m.

Given :

Let x represent the length of the garden and y represent the width of the garden.

Perimeter = 2(x + y)

32 = 2(x + y)

x + y = 16

y = 16 - x

Area (A) = length * width

A = xy

A = x(16 - x)

A = 16x - x²

Maximum area is at dA/dx = 0:

dA/dx = 16 - 2x

0 = 16 - 2x

2x = 16

x = 8.0 m

y = 16 - x = 15 - 7.5 = 8.0 m

The dimensions of the rectangular enclosure for his garden is length of 8.0 m and width of 8.0 m.

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Number of At-the-Door tickets Anna needs to sell to make her goal = 100

Anna is selling pre-sale and at-the-door tickets.

Let 'x' be the number of pre-sale tickets and 'y' be the number of at-the-door tickets.

Price of a pre-sale ticket = $10

Price of an at-the-door ticket = $20

Total price to be raised = $5000

So the equation corresponding is 10x+20y = 5000-----------(1)

Total number of people the venue can hold = 400

Thus the next equation is x+ y = 400---------(2)

From the graph the line with points (0,250) and (500,0) represent the equation (1) since 10 x 0 + 20 x 250 = 5000 and 10 x 500 + 20 x 0 = 5000.

The line with points (0,400) and (400,0) represent the equation (2) as 0+400 = 400 and 400+0 = 400.

So to find x and y we need to solve equations (1) and (2).

10 x (2) ⇒ 10x+10y = 4000-------(3)

Now subtract (3) from (1)

⇒ 10y = 1000

⇒ y = 100

Hence the number of At-the-Door tickets Anna needs to sell to make her goal = 100

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The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.

How to find the volume of a rectangular prism and pyramid?

The formula for the volume of a rectangular prism is:

Volume = Length * Width * Height

The formula for the volume of a pyramid is:

Volume = (Base Area * Height) / 3

The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.

This is because the volume of a rectangular prism is calculated by multiplying its three dimensions together, whereas the volume of a pyramid is calculated by multiplying the base area by the height and dividing the result by 3.

Hence, the volume of the rectangular prism is greater than the volume of the pyramid with the same height and base. This is because the rectangular prism has additional volume in the form of its width, which the pyramid does not have.

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Answer:

Step-by-step explanation:

The ratio of the volume of the pyramid to the volume of the prism is 1.so, the option A. is correct.

Let the base of  the base of a prism is b and the height of the prism is h.

so, the volume of the prism-

                                    V= \(b^{2}\) h

also, given that base of the given pyramid is also b and the height of the pyramid is three times the height of the prism.

                                     h'=3h

so, the volume of the square pyramid-

                                    V'=\(\frac{1}{3}\)\(b^{2}\)h'

                                    V'=\(\frac{1}{3}\)\(b^{2}\)(3h)

                                    V'=\(b^{2}\)h

so, now-

                                  \(\frac{V'}{V}\)=\(\frac{b^{2}h }{b^{2}h }\)

                                   \(\frac{V'}{V}\)= 1

  so. the ratio of the volume of the pyramid to the volume of the prism is 1.                                

The triangle degree measure of ZABC is 180° - 69° - 66. 145°mLABC = 44.855°. (E) mLABC = 44.855°

The given triangle ZABC is shown below.

69° is given and the sum of all angles of a triangle is equal to 180°.

Therefore: mBAC

= 180° - mBCA - mABC

= 180° - 69° - mABC

= 111° - mABC ...(1)

Let's use the law of sines to find the length of side AB.

sin BCA / BC

= sin BAC / BA sin 69° / 50

= sin mABC / ABAB

= sin mABC × 50 / sin 69°AB

≈ 56.042 cm

Now, we will use the law of cosines to find the angle:

mLABC.a² = b² + c² - 2bc cos

ABLAB² = x² + y² - 2xy cos mLABC Cos

mLABC = (x² + y² - LAB²) / 2xycos

mLABC = (31² + 50² - 56.042²) / (2 × 31 × 50)cos

mLABC ≈ 0.41929

mLABC ≈ 66.145°

Therefore, the degree measure of ZABC is 180° - 69° - 66.145°mLABC = 44.855°

Answer: (E) mLABC = 44.855°

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Answer:

Cup A

Step-by-step explanation:

Cup A

Salt: Water = 3:22

Expressed as a percentage

\(\dfrac{3}{22} \times 100 = 13.6\%\)

Proportion of Salt =13.6%

Cup B

Salt: Water = 1:8

Expressed as a percentage

\(\dfrac{1}{8} \times 100 = 12.5\%\)

Proportion of Salt =12.5%

Cup C

Proportion of Salt = 12.75%

Therefore, Cup A has the greatest proportion of salt.

To find the points at which the paths of the two particles intersect, we need to equate the corresponding coordinates of the position vectors.

Given:

Particle 1: F(t) = (1+2t, 1+6t, 1+140)

Particle 2: G(t) = (x, y, z)

Equating the x-coordinates:

1+2t = x

Equating the y-coordinates:

1+6t = y

Equating the z-coordinates:

1+140 = z

From these equations, we can see that x = 1+2t, y = 1+6t, and z = 141.

To find the points of intersection, we need to solve for t. From the x-coordinate equation, we have t = (x-1)/2.

Substituting this value of t into the y-coordinate equation, we have:

1+6((x-1)/2) = y

3x - 3 = 2y

y = (3x-3)/2

Substituting the values of x and y into the z-coordinate equation, we have:

z = 141

Therefore, the points of intersection are given by:

(x, y, z) = (x, (3x-3)/2, 141)

There is no restriction on the x-values, so we can say:

(smaller x-value) = (-∞, (3x-3)/2, 141)

(larger x-value) = ((3x-3)/2, ∞, 141)

Note: The actual numerical values of the points of intersection cannot be determined without more information or specific values for x.

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Answer:

5x-8

Step-by-step explanation:

Two cheeseburgers contain a total of 1120 calories (2 x 560) and one small order of fries contains 230 calories. And three cheeseburgers contain a total of 1680 calories (3 x 560) and two small orders of fries contain a total of 460 calories (2 x 230).

Let's use a system of equations to solve for the caloric content of each item.

Let x be the number of calories in one cheeseburger and y be the number of calories in one small order of fries.

From the first statement, we know that:

2x + y = 1350

From the second statement, we know that:

3x + 2y = 2140

We can use these two equations to solve for x and y. First, we'll solve for y in terms of x by rearranging the first equation:

y = 1350 - 2x

Now we can substitute thisn expression for y into the second equation:

3x + 2(1350 - 2x) = 2140

Simplifying this equation, we get:

3x + 2700 - 4x = 2140

-x = -560

x = 560

So one cheeseburger contains 560 calories. We can plug this value back into either of the original equations to solve for y:

2(560) + y = 1350

y = 230

So one small order of fries contains 230 calories.

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The transformations that the point underwent are given as follows:

The point was reflected over the y -axis and translated up 4 units.

The rule for a reflection over the y-axis is given as follows:

(x, y) -> (-x,y).

Meaning that the x-coordinate of the point has it's signal exchanged.

The original point has the coordinates given as follows:

(5,-2).

After the reflection over the y-axis, the coordinates are given as follows:

(-5, -2).

The rule for a translation up 4 units is given as follows:

(x,y) -> (x, y + 4).

This means that 4 is added to the y-coordinate of the point.

The coordinates of the reflected point after the translation up four units are given as follows:

(-5, -2 + 4) = (-5, 2)

Which are the coordinates of the image in the problem, hence the two transformations are correct.

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To calculate the percentage of books returned based on the number of books returned and the quantity sold, you can divide the number of books returned by the quantity sold and multiply the result by 100 to get a percentage. To insert this formula in cell F7, follow these steps:

To copy the formula to the range F8:F22, click and drag the fill handle (the small square in the bottom-right corner of cell F7) down to cell F22. This will copy the formula to all of the cells in the range, adjusting the cell references as it goes.

The formula to calculate the percentage of books returned based on the number of books returned and the quantity sold is:

=(number of books returned / quantity sold) * 100

To copy the formula from cell F7 to the range F8:F22, follow these steps:

Therefore, This formula is helpful in analyzing sales data for books or any other product, as it allows you to see what percentage of the items sold were returned. This information can be useful for identifying issues with the product or the sales process, and can help businesses make informed decisions about how to improve their products and processes.

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The minimum monthly payment for Brian is $25.

The minimum payment is the smallest amount of money you must pay each month to maintain the status of your account. The statement balance is your total account balance for that billing cycle. The current balance is the sum of your most recent bill plus any charges.

From the information, the minimum monthly payment for Brian's credit card is 3.5% of his balance or $25

Since the balance was $722, the amount will be:

= 3.5% × $722

= 0.035 × $722

= $25.27

Since $25.27 is more than $25, the minimum monthly payment is $25.

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