An engine runs on a mixture of 0.1 quart of oil for every 3.5 quarts of gasoline. you make 3 quarts of the mixture. how much oil and how much gasoline do you use?

Answer: \((z+6)(z+14)\)

x = 20

12.5/10 = 1.25

16 x 1.25 = 20

The probability that two e's are not next to each other when the letters of the word "sixteen" are randomly arranged is approximately 96.67%.

In the word "sixteen," there are three e's. We are asked to find the probability that two e's are not next to each other. Let's first calculate the total number of arrangements of the letters of the word "sixteen."Total number of arrangements = 7! / (2! * 3!) = 420There are three ways in which two e's can be next to each other: ee is the first pair, ee is the second pair, and ee is the third pair. If the first two e's are next to each other, there are five choices for where to place the third e: _e_e_e_, _e_ee_, _ee_e_, _ee_e_, and _eee_. If the second two e's are next to each other, there are four choices for where to place the first e: e_e_e_, e_ee_, _ee_e, _ee_e_, and _eee_. Finally, if the last two e's are next to each other, there are five choices for where to place the first e: e_e_ee, e_e_e_, _ee_e, _ee_e_, and _eee_.So there are a total of 14 arrangements where two e's are next to each other. Therefore, the probability that two e's are not next to each other is:Probability = (total number of favorable outcomes) / (total number of possible outcomes) = (420 - 14) / 420 = 406/420 = 0.9667, or approximately 96.67%.In conclusion, the probability that two e's are not next to each other when the letters of the word "sixteen" are randomly arranged is approximately 96.67%.

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Answer:

x=4

Step-by-step explanation:

(x-1+5)×5=(2+x+4)×4

or, 5×(x+4)=4×(x+6)

or, 5x+20=4x+24

or, 5x-4x=24-20

or, x=4

Answer:

0.62

Step-by-step explanation:

The remainder would be 12 as per the remainder theorem if the function P is defined by P(x) = x³ +7x² - 26x - 72.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

Let   P(x) = x³ +7x² - 26x - 72  ...(i)

Divisor = (x+9)

Apply remainder theorem,

x + 9 = 0

x = -9

Substitute the value of x = -9 in equation (i),

⇒ P(-9) = (-9)³ +7(-9)² - 26(-9) - 72

⇒ P(-9) = (-729) +7(81) - 234 - 72

⇒ P(-9) = -729 + 567 - 234 - 72

⇒ P(-9) = -468

Therefore, the remainder would be -468.

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Answer:

Step-by-step explanation:

90 = 10x+30

60 = 10x

6 = x

B =  ( -3, 4)

Step-by-step explanation:

Given that AB  =  (-5) and AO = (2)

                 AB  =    (1) and  AO =  (3)

Let's say point  A  has coordinates:  

(x1, y1)

(x2, y2)

AO  = (2), we have x1 = 2

AO  =  (3)

y1 = 3, also since AB = (-5)

                                      (1) we have

x2  - x1  = -5 and, y2  - y1 = 1

x2  =  x1  -  5  =  2  - 5  =  -3

y2  = y1   +  1   =  3  +  1  = 4

Therefore, the coordinates of Point (B) are:  

( -3, 4)

AB    =       B  -  A

(-5)    =    ( x )  - (2)

(1)     =    ( y )  -  (3)

( -5)    +    (2)   =    (x)

(1)       +    (3)    =   (y)

(x)       =    ( -5  +  2 )

(y)       =     (1  +  3)

(x)      =     (-3)

(y)      =      (4)

B  =  ( -3, 4 )

I hope this helps!

We can be 98% cοnfident that the true difference in mean amοunt οf fοοd Buster eats when οffered Busted Nuggets and Busted Tenders is between -14.566 and -7.634 grams

Calculate the sample mean difference and the standard errοr οf the difference in οrder tο build the cοnfidence interval fοr the difference in the mean amοunt οf fοοd that Buster cοnsumes when served Busted Nuggets and Busted Tenders.

The sample mean difference is:

X1 - X2 = 152.6 - 163.7 = -11.1 grams.

The standard errοr οf the difference can be calculated as fοllοws:

SE = √(S1²/n1 + S2²/n2)

where S1 and S2 are the sample standard deviatiοns οf the twο grοups and n1 and n2 are the sample sizes.

Substituting the values, we get:

SE = √(4.45²/31 + 5.75²/31) = 1.463

ME = t x (SE) = 2.365 x 1.463 = 3.466

Finally, the cοnfidence interval fοr the difference in mean amοunt οf fοοd Buster eats is:

-11.1 - 3.466 < µ1 - µ2 < -11.1 + 3.466

-14.566 < µ1 - µ2 < -7.634

Hence, we have a 98% cοnfidence level that Buster actually cοnsumes between -14.566 and -7.634 grammes less fοοd οn average when given the chοice between Busted Nuggets and Busted Tenders. This periοd can be understοοd as Buster favοring Busted Tenders because οf the negative.

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Step-by-step explanation:

she has to make one more visit where she will get 60 more points and then she'll have 125.5 points so the equation is :

60+5.5×60=125.5 points

Answer:

60 + 5.5x = 104

Step-by-step explanation:

b + mx = y

b = Initial value

m = slope

Answer:

Therefore, 95 cents is 42.22% of $2.25.

Step-by-step explanation:

To find the percentage of 95 cents in $2.25, we can use the following formula:

Percentage = (part / whole) x 100%

Here, the part is 95 cents and the whole is $2.25. We first need to convert 95 cents to dollars by dividing it by 100:

95 cents / 100 = $0.95

Now we can plug in the values into the formula and solve for the percentage:

Percentage = ($0.95 / $2.25) x 100%

Percentage = 42.22%

Answer:

x\(\geq \\\)8

In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.

In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.

The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.

The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.

This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).

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Answer: yes it is t={1}

PREMISES

16–2t=5t+9

CALCULATIONS

16–2t=5t+9

(16–9)-(2t-2t)=5t+2t+(9–9)

7–0=7t+0

7t=7

7t/7=7/7

t=1/1

t=

1

PROOF

If t=1, then the equations

16–2t=5t+9

16–2(1)=5(1)+9

16–2=5+9 and

14=14 prove the root (zero) t=1 of the statement 16–2t=5t+9

Step-by-step explanation:

Answer:

They are -6 and positive 3

Answer:

y=(3/4)x+6

Step-by-step explanation:

Point 1 (-4,3)

Point 2 (0,6)

To obtain the slope, we apply the formula:

m= (6-3) / (0- (-4))

m= 3 / 4

We replace in the equation y=mx+b.

We take any point.

=> (0,6)

y=mx+b

6=(3/4)(0)+b

b=6

Joining all the terms:

y=(3/4)x+6

a). The percentage of adults that exercise is 42%

b). Percentage of adults are vegetarian is 40%

c). percentage of adults who are vegetarian and exercise is 26%

d). No, because the percentage found in part c is about the same as part b.

Percentage is a number or ratio that can be expressed as a fraction of 100.

According to data, total number of adults = 150

No. of vegetarian who exercise = 39

no. of non vegetarian who exercise = 24

No of vegetarian who don't exercise = 21

a). percentage of adults exercise = 39+24/150×100

=42%

similarly b) percentage adults are vegetarian = 39+21/150×100

= 40%

c) percentage of adults who are vegetarian exercise = 39/150×100

= 26%

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Answer:

1 11/25

Step-by-step explanation:

4/5 ÷ 5/9

= 4/5 × 9/5

= 4×9 / 5×5

= 36/25

= 1 11/25

The answer is a mixed fraction so write 1 first, then next to it put 11/25 in fraction form.

Answer:

1.44

Step-by-step explanation:

Answer:

Step-by-step explanation:

fixed cost = 100

variable cost = 13

soooo....

cost =  (13x + 100)/x

the questions wants to know  when cost  < 22.50

22.5 > (13x+100)/x

look at graph attached ;)

it looks to me like it's at 11

22.5 > (13(11) + 100) / 11

22.5 > 22.09

try 10

22.5 > (13(10) +100)/10

22.5  > 23   not true  so yes.. 11 is when the cost goes below 22.50

Answer:

Y’all the correct answer is 10

The die was rolled 7 times in there 60 times if it is landed on one-11 times, two-9 times, four-12 times, five-12 times, and six - 8 times.

Probabilities are mathematical explanations of the probability of an event occurring or of a proposition being true. The probability of an event is expressed as a number between 0 and 1, where 0 often indicates impossibility and 1 generally indicates certainty.

Given,

Number of times a die rolled=60

And also given that it landed on,

One --- 11 times

Two -----9 times

Four -----12 times

Five -----12 times

Six -------8 times

Total number of times the die was landed on is 52 times.

Therefore, total number of times a die was rolled=60

S0, 52+x=60

x=7

Therefore, the die was rolled 7 times in there 60 times.

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The given expression "the square of a number is 3 less than four times the number" is represented as x² = 3 - 4x and the values of number could be: x1= 0.645 , x2= -4.645

In mathematics, when we refer "square of a number" we mean that the exponent of that number is 2. So we express it mathematically as:

x²

When we express "3 less than" of a number we mean that the number 3 is subtracting that number. So we express it mathematically as: 3 -

x² = 3 -

When we express "four times the number" we mean that the number is exactly 4 times greater than a number or that it contains it 4 times. So we express it mathematically as: 4x

x² = 3 - 4x

Organizing the values, we have a quadratic equation: x² + 4x – 3 = 0

Where:

Solving the quadratic question we get the values for the (x) number

x= {- b ± √ [b² - (4* a*c)]} / (2 *a)

x= {- 4 ± √ [4² - (4* 1*-3)]} / (2 * 1)

x= {- 4 ± √ (16 + 12)} / 2

x= {- 4± √ 28} / 2

x= (- 4 ± 5.29 ) / 2

x1= (- 4 + 5.29 ) / 2

x1= (1,29) / 2

x1= 0.645

x2= (- 4 - 5.29 ) / 2

x2= (9.29) / 2

x2= -4.645

We can check the values, replacing them into the equation:

(x1)² = 3 - 4(x1)

(0.645)² = 3 - 4*(0.645)

0.42 = 0.42

(x2)² = 3 - 4(x2)

(-4.645)² = 3 - 4*(-4.645)

21.58 = 21.58

It is an algebraic equation where the polynomial formed has three terms, one variable has an exponent 2, another in which the variable has exponent 1 and the last term without any variable. Its standard form is:

ax²+ bx + c = 0

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Answer: 46

Step-by-step explanation:

Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

Equations are mathematical statements with the equals (=) sign on each side and two algebraic expressions in the center.

Coefficients, variables, operators, constants, terms, and the equal to sign are just a few of the components that make up an equation. The "=" symbol and terms on both sides are always needed when writing an equation.

calculation

Let s = brittany 's age now

Let t = steve's age now

s = 3t

s + 9 = 2 (t+9)

s + 9 = 2t + 27

s = 2t + 27 - 9

s = 2t + 18

Substitute 3t for s and find t

3t = 2t + 18

3t - 2t = 18

t = 18 yrs is steve's age

then

s = 3(18)

s = 54 yrs is brittany's age

Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

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Answer:

280 cm2

Step-by-step explanation:

1)find the area of square

A=LW

=10×10

=100

2) find the area of triangle

A=B×H÷2

=10×9/2

=45

Coz,there are 4 triangle we multiple by 4

=45×4

=180

3)find the total surface area by adding the two

=100+180

=280cm2

Answer:

SA = [280] cm 2

Step-by-step explanation:

For Lateral Area the formula is 4(1/2 10 x 9)

But the 1/2 makes it 4(1/2 5 x 9)

Then you multiply 5 x 9 = 45 then multiply 45 by the 4 and get 180

Then for Surface Area you put in (180 + 100) = 280

You get the 100 by multiplying 2 of the base numbers together.

The appropriate choice is c. non-probability Sample, as the New York Times is selecting individuals based on convenience and judgment rather than using a random or systematic approach.

In the given scenario, when the New York Times selects a location on the Brooklyn Bridge to interview passersby who are NYC residents about their opinion regarding CUNY funding, it represents a non-probability sample.

Non-probability sampling is a method of selecting participants for a study or survey that does not involve random selection. In this case, the selection of individuals from the Brooklyn Bridge is not based on a random or systematic approach. The New York Times is deliberately choosing a specific location to target a particular group (NYC residents) and gather their opinions on a specific topic (CUNY funding).

This type of sampling method often involves the researcher's judgment or convenience and does not provide equal opportunities for all members of the population to be included in the sample. Non-probability samples are generally used when it is challenging or not feasible to obtain a random or representative sample.

The other options can be ruled out as follows:

a. Media sampling: This term is not commonly used in sampling methodologies. It does not accurately describe the method of sampling used in this scenario.

b. Cluster sampling: Cluster sampling involves dividing the population into clusters and randomly selecting clusters to be included in the sample. The individuals within the selected clusters are then included in the sample. This does not align with the scenario where the sampling is not based on clusters.

d. Random sample: A random sample involves selecting participants from a population in a random and unbiased manner, ensuring that each member of the population has an equal chance of being selected. In the given scenario, the selection of individuals from the Brooklyn Bridge is not based on random selection, so it does not represent a random sample.

Therefore, the appropriate choice is c. non-probability sample, as the New York Times is selecting individuals based on convenience and judgment rather than using a random or systematic approach.

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Thus, the shaded region is the set of solutions for this system of inequalities, and the integers in this region are -4, -3, -2, -1, 0, 1, 2, and 3.

To solve the system of inequalities by graphing, we first need to rewrite each inequality in slope-intercept form, y < mx + b, where y is the dependent variable (in this case, we can use y to represent both 3-2a and 5a), m is the slope, x is the independent variable (in this case, a), and b is the y-intercept.

Starting with the first inequality, 3-2a < 13, we can subtract 3 from both sides to get -2a < 10, and then divide both sides by -2 to get a > -5. So the slope is negative 2 and the y-intercept is 3. We can graph this as a dotted line with a shading to the right, since a is greater than -5:

y < -2a + 3

Next, we can rewrite the second inequality, 5a < 17, by dividing both sides by 5 to get a < 3.4. So the slope is 5/1 (or just 5) and the y-intercept is 0. We can graph this as a dotted line with a shading to the left, since a is less than 3.4:

y < 5a

To find the integers that are in the set of solutions for this system of inequalities, we need to look for the values of a that satisfy both inequalities. From the first inequality, we know that a must be greater than -5, but from the second inequality, we know that a must be less than 3.4. So the integers that are in the set of solutions are the integers between -4 and 3 (inclusive):

-4, -3, -2, -1, 0, 1, 2, 3

To see this graphically, we can shade the region that satisfies both inequalities:

y < -2a + 3 and y < 5a

The shaded region is the set of solutions for this system of inequalities, and the integers in this region are -4, -3, -2, -1, 0, 1, 2, and 3.

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The interpretation is that we are 90% confident that the true difference in the mean daily leisure time between adults with no children and adults with children lies between 0.451 and 2.109 hours.

The given data are: For adults with no children under the age of 18 years, Mean = 5.65 hours Standard deviation = 2.43 hours Sample size, n1 = 40 For adults with children under the age of 18, Mean = 4.37 hours Standard deviation = 1.73 hours Sample size, n2 = 40 The formula to calculate the 90% confidence interval for the difference between two means can be given as:\[\left( {{\bar x}_1} - {{\bar x}_2} \right) \pm {t_{\frac{\alpha }{2},n_1 + {n_2} - 2}}\sqrt {\frac{{s_1^2}}{n_1} + \frac{{s_2^2}}{n_2}}\]where,${{\bar x}_1}$ is the sample mean for group 1,${{\bar x}_2}$ is the sample mean for group 2,${{s_1}}$ is the sample standard deviation for group 1,${{s_2}}$ is the sample standard deviation for group 2,$\alpha$ is the level of significance,$n_1$ is the sample size for group 1,$n_2$ is the sample size for group 2,and $t_{\frac{\alpha }{2},n_1 + {n_2} - 2}$ is the t-value from the t-distribution with (n1 + n2 – 2) degrees of freedom.

Let's calculate the confidence interval as follows: Mean difference, $\left( {{\bar x}_1} - {{\bar x}_2} \right)$= 5.65 − 4.37= 1.28 hours Sample standard deviation for group 1, ${s_1}$ = 2.43 hours Sample standard deviation for group 2, ${s_2}$ = 1.73 hours Sample size for group 1, ${n_1}$ = 40Sample size for group 2, ${n_2}$ = 40 Degree of freedom = $n_1 + n_2 - 2$= 40 + 40 – 2= 78$\alpha$ = 0.1 (90% confidence interval, $\alpha$ = 1 – 0.9 = 0.1)Using the t-table or calculator with the given values, we get:$t_{\frac{\alpha }{2},n_1 + {n_2} - 2}$ = t0.05, 78 = 1.665 (approximately)Substituting the given values in the formula, we get:\[\left( {{\bar x}_1} - {{\bar x}_2} \right) \pm {t_{\frac{\alpha }{2},n_1 + {n_2} - 2}}\sqrt {\frac{{s_1^2}}{n_1} + \frac{{s_2^2}}{n_2}}\] = $1.28 \pm 1.665\sqrt {\frac{{2.43^2}}{40} + \frac{{1.73^2}}{40}}$= $1.28 \pm 0.829$= (0.451, 2.109)

Therefore, the 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children is (0.451, 2.109) hours.

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We can also say that adults with no children have, on average, between 0.50 hours and 2.06 hours more leisure time per day than adults with children under the age of 18.

The 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children is (-1.23, -0.04).

We are to construct a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children.

We are given the following information:

u1 = mean daily leisure time of adults with no children

= 5.65 hours

σ1 = standard deviation of daily leisure time of adults with no children

= 2.43 hours

n1 = sample size of adults with no children

= 40

u2 = mean daily leisure time of adults with children

= 4.37 hours

σ2 = standard deviation of daily leisure time of adults with children

= 1.73 hours

n2 = sample size of adults with children

= 40

We can find the standard error (SE) of the difference in means as follows:

SE = sqrt [ (σ1^2 / n1) + (σ2^2 / n2) ]

SE = sqrt [ (2.43^2 / 40) + (1.73^2 / 40) ]

SE = sqrt (0.1482 + 0.0752)

SE = sqrt (0.2234)

SE = 0.4726

We can now use the formula for a confidence interval of the difference in means as follows:

CI = ( (u1 - u2) - E , (u1 - u2) + E )

where

E = z*SE and z* is the z-score for the level of confidence.

Since we want a 90% confidence interval, we look for the z-score that corresponds to the middle 90% of the normal distribution, which is found using a z-table or calculator.

For a 90% confidence level, the z* value is 1.645,

so:E = 1.645 * 0.4726E = 0.7779

Plugging in the values, we have:CI = ( (5.65 - 4.37) - 0.7779 , (5.65 - 4.37) + 0.7779 )CI = ( 1.28 - 0.78, 1.28 + 0.78 )CI = ( 0.50, 2.06 )

The 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children is (0.50, 2.06).

This means that we are 90% confident that the true mean difference in leisure time between the two groups of adults falls between 0.50 hours and 2.06 hours.

Since the interval does not include zero, we can conclude that the difference in means is statistically significant at the 0.10 level. We can also say that adults with no children have, on average, between 0.50 hours and 2.06 hours more leisure time per day than adults with children under the age of 18.

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The measure of smaller angle is found to be 72° .

Two angles are called supplementary angles if their sum is two right angles, that is 180∘. Each angle is called the supplement of the other. For example, the supplement of 95°=180°−95°=85°.

Given that,

The larger angle is 1. 5 times the smaller angle.

Lets take ,

The smaller angle = x

Then , the larger angle will be = 1.5 x  ( according to question)

Now,

we know that, the sum of two supplyementary angle = 180°

Therefore,

   x + 1.5 x = 180

⇒2.5 x = 180

⇒ x = 180 / 2.5

⇒ x = 72

Then ,

the larger angle will be 1.5 x = 108.

Hence, The measure of smaller angle is found to be 72° .

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Answer:

20 Feet

Step-by-step explanation:

If the trucks are all 7 feet tall, and 6 feet wide, then we can find out how long we need the truck to be by using this equation:

(l = length)

7 × 6 x l = 840

Or we can simply multiply 6 and 7 then divide 840 by that number.

6 × 7 = 42

840 ÷ 42 = 20

The truck would need to be 20 feet long to carry all of your furniture.

Answer: x= 8   y= 17

Step-by-step explanation: 6*8 = 48+11=59

3*17=51+8=59

Answer:

x = 11.375

y = 23.75

Step-by-step explanation:

Corresponding angles:  A pair of angles that are in the same relative position at each point where a straight line intersects two other straight lines.

If the two lines are parallel, the corresponding angles are equal. 

Therefore:

⇒ (6x + 11)° = (3y + 8)°

⇒ 6x + 11 = 3y + 8

⇒ 6x + 3 = 3y

⇒ 3y = 6x + 3

Angles on a line sum to 180°.  

Therefore:

⇒ (3y + 8)° + (10x - 13)° = 180°

⇒ 3y + 8 + 10x - 13 = 180

⇒ 3y + 10x = 185

⇒ 3y = 185 - 10x

Substitute the first equation into the second equation and solve for x:

⇒ 6x + 3 = 185 - 10x

⇒ 16x = 182

⇒ 16x = 182

⇒ x = 11.375

Substitute the found value of x into one of the equations and solve for y:

⇒ 3y = 6(11.375) + 3

⇒ 3y = 68.25 + 3

⇒ 3y = 71.25

⇒ y = 23.75