A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1525 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?

Answer:

[tex]\boxed{\sf y=37^o}[/tex]

[tex]\boxed{\sf x=74^o}[/tex]

[tex]\boxed{\sf z=25^o}[/tex]

Step-by-step explanation:

Let's first solve for y:-

*Linear pairs are supplementary angles, meaning there sum should be 180° *

[tex]\sf 2y^o+106^o=180^o[/tex]

[tex]\sf 2y=180-106[/tex]

[tex]\sf \cfrac{2y}{2} =\cfrac{74}{2}[/tex]

[tex]\boxed{\sf y=37^o}[/tex]

*Consecutive angles are also supplementary angles = 180°*

[tex]\sf x=2y[/tex]

[tex]\sf x=2(37)[/tex]

[tex]\boxed{\sf x=74^o}[/tex]

By corresponding angles,

[tex]\sf 4z+6=106[/tex]

[tex]\sf 4z+6-6=106-6[/tex]

[tex]\sf \cfrac{4z}{4} =\cfrac{100}{4}[/tex]

[tex]\boxed{\sf z=25^o}[/tex]

_____________________

Hope this helps!

Have a good day!

The subtotal before the surcharge and the sales tax is $12.25   .

In the question ,

it is given that ,

the total amount paid for the taxi ride = $13.73

sales tax percent charged = 4%

amount of surcharge = $1 .

let the subtotal before the tax and surcharge be "x"

the amount paid by the customer can be represented by the equation ,

total amount = cost + 4% of cost + surcharge

Substituting the values from above , we get

13.73 = x + 4% of x  + 1

4% of x + x = 13.73 - 1

0.04x + x = 12.73

1.04x = 12.73

x = 12.73/1.04

x = 12.24038

x ≈ 12.25

Therefore , The subtotal before the surcharge and the sales tax is $12.25   .

The given question is incomplete , the complete question is

A taxi ride cost a customer a total of $13. 73, which included 4% , percent sales tax and then a $1dollar surcharge. What was the subtotal before the surcharge and sales tax ?

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The unit rate of the number of cups of water per cup of lime juice are;

Jaylan;

Wanchen;

Unit rate indicates the rate of an item for a quantity of one of another item such that when the quantitative relationship is expressed as a ratio, the denominator will be one.

The content of limeade Jaylan makes are;

The ingredient of the limeade Wanchen makes are;

The unit rate of water (cups) per lime juice (cups) is therefore;

Jaylan; 34 cups of water for every 15 cups of lime juice

Therefore;

34/15 cups of water for 1 cup of lime juice

34/15 = 2.2[tex]\overline 6[/tex]

The unit rate of the drink Jaylen makes is 2.2[tex]\overline 6[/tex] cups of water per cup of lime juice

Wanchen; 35 cups of water per 12 cups of lime juice

Therefore;

35/12 cups of water per cup of lime juice

35/12 = 2.91[tex]\overline{6}[/tex]

The unit rate is 2.91[tex]\overline 6[/tex] cups of water per cup of lime juice

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Answer:
D

Step-by-step explanation: 5 are crossed rows by 3 and then 7 by 5 are shaded in and than is 2 different numbers in together multiplied equals 1.500 which is D

Using the percentage, the truck is 342 inches long. So the option C is correct.

In the given question we have to find the length of the truck.

As given that, a car is 180 inches long.

A truck is 90% longer than the car.

The length of the car is 180 inches.

Truck is longer than the cars is 90%.

So the length of the truck = 180+180*90%

The percentage represent in the ratio of 100.

So the length of the truck = 180+180*90/100

Simplifying

The length of the truck = 180+162

The length of the truck = 342

Hence, the truck is 342 inches long. So the option C is correct.

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Answer:

Step-by-step explanation:

Ok:

1. First write as equation!

x/3=4.5

2. Isolate the variable on the left side. Remember if a variable or number goes over equal sign, it becomes opposite

x/3=4.5

x=4.5*3

x=13.5

3. Double Check as always!!

13.5/3= 4.5

TRUE

Answer: 13.5

Answer:

13.5 is the answer ..hopefully this helps

Answer:

Step-by-step explanation:

she will pay $80 in interest.

If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.

Let T be the time and L be the Labor (Number of people working on the bridge).

T ∞ 1/√L  (Inverse relationship)

T = K/√L                   ----------------------------- (1)

Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.

According to the question,

Time (T) = 75 days    and

labor (L) = 09

From the equation (1), we get,

    T = K / √L

⇒ 75   = K/√9

⇒ 75= K/3

⇒ K= 225

First, the relationship between these variables is:

                       T = 225/√L

Therefore, how long it will take 25 people to do it means that we should look for the time.

                           T=225/√L

                      ⇒  T= 225/√25

                      ⇒  T= 225/5

                      ⇒  T= 45 days.

therefore, 25 people needs 45 days to complete the job.

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According to the central limit theorem, given a population with mean μ and standard deviation σ, if a suitably large random sample (n ≥ 30) is drawn from the population with permutation, the distribution of the sample mean will be approximately normally distributed. Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.

Then the mean of the sample mean is given by

[tex]\mu_ {x} =\mu[/tex]

and the standard deviation of the sample mean is given by

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} }[/tex]

The standard deviation of the sample mean is inversely proportional to the sample size n

so if n increases, the standard deviation decreases and vice versa.

(a) Sample size increased from 64 to 196.

As mentioned above, the standard deviation decreases as the sample size increases.

Therefore, increasing the value of n from 64 to 196 reduces the standard deviation of the sample mean.

n = 64 sample mean standard deviation:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{64} } \\\\\sigma_{x} = 0.7[/tex]

n = 196 sample mean standard deviation:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{196} } \\\\\sigma_{x} = 0.4[/tex]

sample mean standard deviation decreased from 0.7 to 0.4 n was 64 When it increased to 196.

Therefore the variance is also decreases.

(b)

decreace the sample size, increase the standard deviation.

Therefore, as the value of n decreases from 784 to 49, the standard deviation of the sample mean increases.

Standard deviation of sample mean for n = 784:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{784} } \\\\\sigma_{x} = 0.2[/tex]

Standard deviation of sample mean for n = 49:

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{49} } \\\\\sigma_{x} = 0.8[/tex]

Standard deviation of sample mean increased from 0.2 to 0.8 while, n increased from 784 Then 49 decreases.

Therefore, the variance is also increases.

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Answer:

31. (25 - 8) x 3 = 51

32.  9 + 4 x (5 - 3) = 17

Step-by-step explanation:

grouping symbols

31.) 25 - 8 x 3 = 51

(25 - 8) x 3 = 51

Do the parentheses first

17 * 3 = 51

51=51

32.) 9 + 4 x 5 - 3 = 17

9 + 4 x (5 - 3) = 17

Parentheses first

9 + 4 * 2 = 17

Multiply

9+8 = 17

Add

17=17

Answer:

Since 1 scoop of ground coffee makes 1 cup of coffee, Andy can make 24 cups of coffee from the jar.

Step-by-step explanation:

Answer:   b

Step-by-step explanation:

Answers. 230 is the answer that I got

The age of the mammal is 3567 years.

Change the given numbers' letters in the equation to match:

N ="NOekt"

N-amount following t years

If not, the initial sum

K=0.0001t, where t=the number of years

Change the given numbers' letters in the equation to match:

0.70 = 1 * e^-0.0001t

Consider the two sides' logarithms:

t = -0.1549 / (-0.0001 * 0.43429) log0.70 = loge-0.0001t -0.1549 = -0.0001t * 0.43429 t = 3566.74

The age is 3,567 years, rounded to the nearest year.

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The points scored by Mrs. Dellett  on her 9th attempt is 210.

Given, Mrs. Dellett took up archery as a hobby.

On her first attempt she scored 18 points.

then every attempt after that, she increased her score by 24 points.

first attempt = 18 points

after this her score increased to 24 points on every attempt.

second attempt = 18+24 = 42

third attempt = 42+24 = 66

fourth attempt = 66+24 = 90

fifth attempt = 90 + 24 = 114

sixth attempt = 114 + 24 = 138

seventh attempt = 138 + 24 = 162

eight attempt = 162 + 24 = 186

ninth attempt = 186 + 24 = 210

Hence the option D is correct.

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The height of the block that has dimensions of 10 cm and 12 cm and a volume of 1,800 cubic centimeters is 15 cm

A rectangular prism is a figure that has six faces that are rectangles.

The dimensions of the rock are;

Width of the rock = 10 cm

Length of the rock = 12 cm

Volume displaced by the rock = 1,800 cubic centimeter

Height of the rock = Required

Let h represent the height of the rock, we get;

Volume of a rectangular prism, V = Length × Width × Height

Volume of the rock = 10 × 12 × h = 1,800

h = 1,800 ÷ (10 × 12) = 15

Where the volume of the rock is 1,800 cubic centimeter, the height of the rock is 15 centimeters

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The 28th percentile for the number of chocolate chips in the bag is 1192.206

To determine the 28th percentile for the number of chocolate chips in the bag, we find the z-score for the 28th percentile.

Found using a z-table or z-calculator, the z-score for the 28th percentile is -0.583

The formula for finding X (the number of items in a given percentile) is:

X = M + Z(S.D.)

Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.

So for the 28th percentile,

X = 1261 + (-0.583)(118)

X = 1261 - 68.79 = 1192.206

Hence the 28th percentile id 1192.206

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Answer:40%

Step-by-step explanation: Take 16 divided by 40 and you get .04, which equals 40 percent. Another way to think about it is this way: if 40 miles is the total distance, every 4 miles is 10% of the total. So 16 has to be 40%.

The polynomial function with third degree, zeros of −3, −1, and 4, and a y-intercept of −13 is y = -13/12 (x³ - 13x + 12)

Polynomial function:

polynomial function means a functions of single independent variables, in which variables can occur more than once, raised to an integer power.

Given,

Third-degree, with zeros of −3, −1, and 4, and a y-intercept of −13.

And we need to construct  a polynomial function with the stated properties and reduce all fractions to lowest terms.

We know that the standard form for the third degree polynomial function is written as,

=> y = K (x + zeros1) (x + zeros2) (x + zeros3)

The third degree, zeros of the function is -3, -1 and -4.

Now, we have to apply it on the general form,

=> y = K (x -3) (x - 1) (x + 4) ----------------------(1)

Here we know the value of y intercept is -13 then the value of x is 0.

So, it can be written as,

=> -13 = K(0 - 3) (0 - 1) (0 + 4)

=> -13 = K (12)

Therefore, the value of K = -13/12

Now, apply the values on the equation (1), then we get,

=> y = -13/12 (x -3) (x - 1) (x + 4)

Therefore, the third degree polynomial function is,

=> y = -13/12 (x³ - 13x + 12)

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The equation to represent the cost is C =  8 + 1.50x + 0.75y.

To write an equation that represents the cost of a pizza.

An equation that represents the cost of a pizza will be

C = 9 + 1.75x + 0.50y

   Fixed cost = $9

   Cost of additional inch = 1.75x

   Cost of additional topping = 0.50y

Total cost (C) will then be:

= 9 + (1.75 × x) + (0.50 × y)

C = 9 + 1.75x + 0.50y

Hence the answer is, the equation to represent the cost is C =  8 + 1.50x + 0.75y.

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The probability that he gets four or fewer questions correct is 0.9984

Let p be probability of getting correct answer and q be probability of getting in correct answer.

Number of trails :  n = 6

Number of Successes : x = 4

By using binominal distribution ,

P(x≤4) = 1 - P(x>4)

= 1 - [P(x = 5) + P(x = 6)]

= 1 - [ ⁶C₅ p⁵ q +⁶C₆ p⁶ ]

solving combination ,

= 1 - [ 6 × 4/(5⁶) + 1 /(5⁶) ]

= 1 - (24 + 1 / 625)

= 1 - 25 / 625

= 624/625 = 0.9984

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If she sold the gold bracelet at $2012, the profit would be $1212

Let  original price of the gold bracelet be x

Mrs Tan wanted to make a profit of 52%

The selling price would be $1216

Selling price = x + 52% of x

1216 = x + (52/100)x

1216 = 152/100x

x = 1216(100/152)

x = 800

The original price is $800

The price at which she sells the gold bracelet is 2012

Profit = selling price - original price

= 2012 - 800

= 1212

Therefore, if she sold the gold bracelet at $2012, the profit would be $1212

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Answer:

16.2

Step-by-step explanation:

16.18034 to 1 decimal place = 16.2

If it 2 decimal place =16.18

Answer:

ASA

Step-by-step explanation:

1) the angles are congruent where they intercept in blue

2) the sides that are congruent are between the two congrunet  angles  the blue ones and the given ones

Check the picture below.

[tex]tan(x) =\cfrac{\stackrel{opposite}{10}}{\underset{adjacent}{4}}\implies tan(x)=\cfrac{5}{2}\implies x=tan^{-1}\left( \cfrac{5}{2} \right)\implies x\approx 68.20^o[/tex]

Make sure your calculator is in Degree mode.

The slope of the line is 3/2, Equation of the line in point-slope form ( y - 10) = 3/2 (x-2), and The equation of the line in slope-intercept form

y = (3/2) x - 13

Using the slope formula, calculate the slope. To find the y-intercept (b), use the slope and one of the points.

Once you know the values for m and b, you can enter them into the slope-intercept form of a line (y = mx + b) to derive the line's equation.

Therefore,

A line goes through the points (2,10) and (-2,4).

Slope = (y2-y1)/(x2 -x1)

= (4 - 10) / (-2 - 2)

= -6/-4 = 3/2

The equation of the line in point-slope form using the point (2,10)

Slope  = 3/2

equation of the line in point slope form :

(y - y1) = m (x -x1)

(y - 10) = 3/2 (x-2)

y = mx + c

Simplifying the above equation, then we get

2 = 3/2 × 10 + c

c = 2 - 15

c = -13

equation of the line is

y = (3/2)x - 13

2y = 3x - 26

the slope-intercept equation of the line

y = (3/2) x - 13

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Answer: x = 12, y = 15

Step-by-step explanation: 12/15 reduces to 4/5 because 12 divided by 3 is 4 and 15 divided by 3 is 5. 12 + 3 is 15 so if you add 3 to the numerator, you get 15/15, which is equal to 1.

The relative displacement of the given case is δ = [tex]\frac{ph}{Et(d2-d1)}ln(\frac{d2}{d1} )[/tex]

Given;

To get the axial load-related relative displacement of one end of the tapered plate concerning the other end.

Let 'd' be the displacement;

We know,

[tex]w = d1 + \frac{(d2-d1)x}{h} = \frac{d1h+(d2-d1)x}{h}[/tex]

To calculate the relative displacement;

δ = [tex]\int\limits {\frac{p(x)}{A(x)E} } \, dx =p/E \int\limits {\frac{1}{\frac{d1h+(d2-d1)x}{h}t } } \, dx[/tex]

δ = [tex]ph/Et\int\limits^h_0 {\frac{dx}{d1h+(d2-d1)x} } \,[/tex]

δ = [tex]\frac{ph}{Et(d2-d1)}[ln(1+\frac{d2-d1}{d1}) ][/tex]

δ = [tex]\frac{ph}{Et(d2-d1)}ln(\frac{d2}{d1} )[/tex]

Therefore, the Relative displacement of the given case is δ = [tex]\frac{ph}{Et(d2-d1)}ln(\frac{d2}{d1} )[/tex]

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