billie has 2 [tex]\frac{1}{4}[/tex] bars of chocolate she eat 5/8 of a bar how much does she have left. give your answer as a mixed number in its simplest form

The interval reflects 95% of the critical reading scores is 430 t 230.

What is intervals?

Interval is the period of time between two points.

As per the given scenario

1.6 million students took the critical Reading portion of the SAT exam. The mean score, the modal score, and the standard deviation were calculated to be 115, respectively. 496,430,

95% confidence intervals

(Mu - 6.7-Mu+6.7)

(430-115×2 , 430+115×2)

By adding or substracting

( 430-230, 430+230)

So interval (430±230)

Thus,

The interval= 430±230.

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Answer: 0.6

Step-by-step explanation:

9/15 = 0.6

$9 / 15 cookies = $0.6 cents per cookie

The first step performed by Daniela was that she subtracted 1 / 2 x from both sides of the equation.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

In other words, equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, Daniela is trying to solve an equation for x.

1/2 x + 3 = 7/2 x + 5

The variable of the equation is x. The variable of an equation is a number represented with letters.

Hence, the first step performed by Daniela is as follows:

Subtract 1 / 2 x from both sides of the equation

1/2 x + 3 = 7/2 x + 5

1/2 x - 1 / 2 x + 3 = 7/2 x - 1 / 2 x + 5

3 =  7/2 x - 1 / 2 x + 5

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Answer:

Substitute x = 4 into the equation.

f(4) = 2(4)² - 6

= 2(16) - 6

= 32 - 6

= 26

[tex]\fbox{356}[/tex]

[tex](5\times4\times5\times3)+56[/tex]

[tex]5\times4=20\\5\times3=15\\20\times15=300[/tex]

[tex]300+56=356[/tex]

Answer: 356

Step-by-step explanation:

-start by grouping numbers into smaller portions (ex. the 5x5)

-5x5=25

-4x3=12

-Now we have 25x12.

-10x25=250, now add two more 25's

-250+50=300 or 25x12=300

-Add 56 to get 356

The interquartile range IQR for the given data set is IQR=10

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.

Finding the median, lower quartile, and upper quartile of a given set of data (Q2, Q1, and Q3) is the first stage in creating a box-and-whisker figure. Now that you know how to calculate the interquartile range (IQR). The distance between the upper and lower quartiles is known as the interquartile range.

Lower data set:

70 73 81 84

Q1=73+81/2=77

Middle data set

65 70 75 80

Q2= 70+75/2=72.5

Upper data set

85 87 90

Q3=87

IQR=Q3-Q1=87-77=10

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Answer:

4

Step-by-step explanation:

Given expression:

[tex]\left(2-\log_{\sqrt{2}}10\right)\left(2-\log_{\sqrt{5}}10\right)[/tex]

[tex]\textsf{Apply the radical rule}: \quad \sqrt{a}=a^{\frac{1}{2}}[/tex]

[tex]\implies \left(2-\log_{2^{\frac{1}{2}}}10\right)\left(2-\log_{5^{\frac{1}{2}}}10\right)[/tex]

[tex]\textsf{Apply the log rule}: \quad \log _{a^n}(x)=\frac{1}{n}\log _a\left(x\right),\:\quad \:a > 0[/tex]

[tex]\implies \left(2-\dfrac{1}{\frac{1}{2}}\log_{2}10\right)\left(2-\dfrac{1}{\frac{1}{2}}\log_{5}10\right)[/tex]

[tex]\implies \left(2-2 \log_{2}10\right)\left(2-2\log_{5}10\right)[/tex]

Rewrite 10 as 2 · 5 and 10 as 5 · 2:

[tex]\implies \left(2-2 \log_{2}(2 \cdot 5)\right)\left(2-2\log_{5}(5 \cdot 2)\right)[/tex]

[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\implies \left(2-(2 \log_{2}2+2\log_2 5)\right)\left(2-(2\log_{5}5 +2\log_52)\right)[/tex]

[tex]\implies \left(2-2 \log_{2}2-2\log_2 5\right)\left(2-2\log_{5}5 -2\log_52\right)[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies \left(2-2(1)-2\log_2 5\right)\left(2-2(1) -2\log_52\right)[/tex]

[tex]\implies \left(2-2-2\log_2 5\right)\left(2-2 -2\log_52\right)[/tex]

[tex]\implies \left(-2\log_2 5\right)\left(-2\log_52\right)[/tex]

Multiply:

[tex]\implies 4 \cdot \log_2 5 \cdot \log_52[/tex]

[tex]\textsf{Apply the log rule}: \quad \log _{a}(x) \cdot \log_{x}(a)=1[/tex]

[tex]\implies 4 \cdot 1[/tex]

[tex]\implies 4[/tex]

Answer: 487.5

Step-by-step explanation:

Formula for Simple interest is

S.I = (P×R×T)/ 100

so, we are given with

P = 1500 ; R = 5% ;

T = 2 years 6 months    

*here we need to convert 6 months in to years

so,

6 months = 1/2 year

T = 6 year + 1/2 year = 13/2 years

Now putting these values in formula

We get;

S.I = (1500×5× 13/2) / 100

Ans : 487.5

The Missing number for each fraction is ---

a) 3/7 = 12/28

b)5/8 = 25/40

c)3/4 =12/16

d)7/3 = 14/6

Fraction:

A fraction (from Latin: fracturs, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples {1}/{2}} and ) consists of a numerator, displayed above a line (or before a slash like 1⁄2), and a non-zero denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.

Given that

a) [tex]\frac{3}{7}[/tex] = 12/_

  let x

3/7 = 12/x

3x = 84

x = 28

3/7 = 12/28

b) x/8 = 25/40

40x = 200

x = 5

5/8 = 25/40

c)3/4 = x/16

4x =48

x =12

3/4 =12/16

d)7/x = 14/6

42 = 14x

x = 3

7/3 = 14/6

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Answer:

6,561

Step-by-step explanation:

((3*3)²)²

((9)²)²

(81)²

6,561

Answer:

Step-by-step explanation

answer:6561

3 times 3 = 9

9^2=81

81^2=6561

Answer:

The correct answer is (0) and (-10)

Step-by-step explanation:

The standard form of this equation is (x-a)(x-b)=0

so, here given equation is : x(x+10)=0

For solving the equation, equate both the LHS parts equals to RHS i.e. :

x(x+10)=0

x=0 &                          (x+10)=0 or x=(-10)

The slope of line perpendicular to line 3x - 6y = 90 is -2.

Slope-Intercept form of equation => y = mx + c

Slope = m

Given equation,

3x - 6y = 90

 x - 2y = 30

      2y = x - 30

        y = x/2 - 15

        y = (1/2)x + (-15)

Here, slope = m1

                   = 1/2

For line perpendicular slope will be negative reciprocal of the slope of given line.

Therefore, slope of other line = m2

                                                 = -1/m1

                                                 = -2

Hence, slope of line perpendicular to line 3x - 6y = 90 is -2.

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Answer:

95

Step-by-step explanation:

x = 38 over 0.4 = 95

38 over x 100=40%

The cost incurred by Rachael's restaurant as fixed, variable or mixed are given below.

What is restaurant?

A restaurant is a location where you can consume food while paying for it. In restaurants, a waiter or waitress will typically bring your food to your table. Breakfast, lunch, and dinner are all offered at the restaurant. The restaurant's food was delectable, and the waitstaff was courteous.

Given:

Rachael’s Restaurant, a fast-food restaurant company, operates a chain of restaurants across the nation.

Each restaurant employs eight people; one is a manager paid a salary plus a bonus equal to 4 percent of sales.

Other employees, two cooks, one dishwasher, and four servers, are paid salaries. Each manager is budgeted $3,000 per month for advertising costs.

The cost incurred by Rachael's restaurant as fixed, variable or mixed are,

a. Advertisement c cost relative to number of customers      Fixed

b. Rental cost relative to number of restaurant                    Variable

c. Cooks salaries relative to number of customer             Fixed

d. Cost of Supplies (cups, plates, spoons, etc.) relative

to number of customer                                                     Variable

e. Manager's compensation relative to number of customer Mixed

f. Servers' salaries relative to number of Restaurants        Variable

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Complete question:

Complete question is attached below.

We are 95% confident that the true slope of the relationship between weight and number of gogles for all piknits lies between 5.68, 7.92.

The population parameter's (1 - α)% confidence interval denotes a probability of (1 -α ) that the interval contains the parameter's true value.

Or, the parameter's (1 -α )% confidence interval means that there is (1 - α)% certainty or confidence that the interval contains the genuine parameter value.

Assume that the weight's 95% confidence interval is (p1, p2).

The mean weight's 95% confidence interval

The likelihood that the true means fall within this range is 0.95.

95 of these intervals will contain the actual mean weight if 100 of these intervals are generated using 100 identical-sized samples.

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Complete question :

Suppose the confidence interval was (5.68,7.92). What is the correct interpretation of this interval? The true slope of the relationship between weight and number of gogles lies between 5.68 and 7.92 We are 95% confident that the true slope for the relationship between weight and number of gogles for our sample of piknits lies between 5.68 and 7.92. There is a 95% chance that the true slope of the relationship between weight and number of gogles lies between 5.68 and 7.92. We are 95% confident that the true slope of the relationship between weight and number of gogles for all piknits lies between 5.68 and 7.92.

If the farmer plans to fence a rectangular pasture adjacent to a river than the dimensions that is required for the least amount of fencing is  length = 900 m and width = 450 m  .

In the question ,

it is given that ,

the farmer is planning to fence the rectangular pasture adjacent to the river ,

the area of the pasture is = 405000 square meter .

let the length of the pasture = "y"

let the width of the pasture be = "x" ,

since only three side is fenced , the required perimeter is = 2x + y ;

given that area ⇒ x*y = 405000

y = 405000/x  ;

So , the perimeter equation becomes ;

p = 2x + 405000/x

differentiating and equation to 0 we get ;

p' = 2 - 405000/x²

2 - 405000/x² = 0 ;

2x² = 405000

x² = 202500 ;

x = 450 , putting in perimeter equation ,

we get ; y = 900 .

Therefore , the dimension is length = 900 m and width = 450 m.

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Answer:

B

Step-by-step explanation:

The function is increasing anywhere the slope is positive.  This corresponds to the intervals -4<x<-2 and 0<x<2.  So, answer B is correct.

The graph of the function is attached below:

The asymptote of the function is:

(-3 log(-x-4)/log2)-8  →∞ as x→ -4

Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. The sets X and Y are referred to together as the function's codomain and domain, respectively.

Al-Biruni and Sharaf al-Din al-Tusi were two Persian mathematicians who are credited with developing the earliest known approach to the concept of function. The basic conception of functions was the relationship between fluctuating quantities and other variables. An illustration of this is how time affects a planet's position. The idea was developed historically with the infinitesimal calculus towards the end of the 17th century, and until the 19th century, the functions that were taken into consideration were differentiable.

Given function is,

f(x)= -3 log₂ (-x-4) - 8

The graph of the function is attached below:

The asymptote of the function is:

(-3 log(-x-4)/log2)-8  →∞ as x→ -4

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The equation representing the total number of wheels is given as follows:

u + 2b = 22.

This problem is modeled by a system of equations, for which the variables are given as follows:

There is a total of 15 seats, hence, considering that each of the objects have one seat, we have that:

u + b = 15.

There is a total of 22 wheels, and we have that:

Then the equation representing the total number of wheels is given as follows:

u + 2b = 22.

The problem asks for the equation representing the total number of wheels in this problem.

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f(t) =  [tex]0.01 ( 2 )^{t}[/tex] is  which investment will eventually have the greater value.

What investment means?

An asset or object purchased with the intention of generating income or appreciation is referred to as an investment. An asset's value increasing over time is referred to as appreciation.

                               When a person buys a product as an investment, they don't intend to utilize it right away; instead, they plan to use it to make money later on.

F(t) = [tex]a(b)^{t}[/tex]

option a -                      a = 5

                                b = 1.5

                        f(t) = 5(1.5)

option b -                    a  = 0.01

                                  b = 2

               f(t) =  [tex]0.01 ( 2 )^{t}[/tex]

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The number of hours to breakeven will be 5 hiurs

The breakeven is the point at which the cost and the revenue are equal.

Since Mitch sells thingamabobs. His revenue is modeled by the function R(h) = 5h+ + 8 for every h hours he spends working and his overhead cost is modeled by the function C'′(h) = h² + 7h − 16.

This wll be:

Revenue = Cost

5h + 8 = h² + 7h - 16

Collect like terms

h² + 7h - 5h - 16 = 0

h² - 2h - 16 = 0

Solving the equation will give h as 5.

The number of hours will be 5 hours.

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The correct options for the given parts are as follows

(a) Two-sample t-test.

(b) x1 bar - x2 bar = 12.1 - 11.2 = 0.9

(c) p - value = 0.031

(d) The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.

(e) The test result is statistically significant.

(f) Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.

What is sample statistics?

Any number calculated from your sample data is referred to as a sample statistic (or simply a statistic). The sample average, median, sample standard deviation, and percentiles are a few examples. Because a statistic is based on data obtained through random sampling, which is a random experiment, it is a random variable.

a) Since there are two independent samples and we want to compare population means. We must use: Two-sample t-test.

b) The value of the sample statistic to test those hypotheses is:

x1 bar - x2 bar = 12.1 - 11.2 = 0.9

c) This is two-tailed test. For p-value, use excel formula =TDIST(2.169,202,2).

p - value = 0.031

d) Since p-value is less than 0.05, correct option is:

The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.

e) Since p-value is less than 0.05, correct option is:

-The test result is statistically significant.

f) Since null hypothesis is rejected, we might have been made Type I error. The correct option is:

-Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.

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Answer:

March 4

Step-by-step explanation:

The fifth Thursday must happen 4 weeks after the first one. That means that the 5th Thursday is 28 days after the first one.

Feb 1 + 28 days = Feb 29

Feb 1, Thursday

Feb 8, Thursday

Feb 15, Thursday

Feb 22, Thursday

Feb 29, Thursday

Mar 1, Friday

Mar 2, Saturday

Mar 3, Sunday

Mar 4, Monday

Answer: March 4

The pail was pale because it was most likely made from a light-coloured material such as plastic or metal.

It is not clear why the pail was pale. The phrase "the pail was pale" does not make sense in the context of the properties of a pail. Pails are typically made of metal, plastic, or some other type of material and do not have a color or shade.

It is possible that you meant to ask a different question or that the phrase "the pail was pale" was intended as a joke or a play on words. Without more context, it is not possible to provide a meaningful answer.

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Answer:

=6x3+15x2y−46x2−115xy+80x+200y

Step-by-step explanation:

-2/3 to the 5th power is equal to -0.008. To do this, we first need to raise -2/3 to the 1st power.

-2/3 to the 5th power can be calculated by raising -2/3 to the 5th power. To do this, we first need to raise -2/3 to the 1st power. This is equal to -2/3. We then need to multiply this result by itself four more times (since it is to the 5th power).

-2/3 * -2/3 = 4/9

4/9 * -2/3 = -8/27

-8/27 * -2/3 = 16/81

16/81 * -2/3 = -32/243

-32/243 * -2/3 = 64/729

Therefore, -2/3 to the 5th power is equal to 64/729. To simplify this, we can divide the numerator and denominator by 64. This gives us 1/11.5 which is equal to -0.008.

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Answer:

B. 2x - 5000

Step-by-step explanation:

She makes x now.

2 times x is 2x.

2 times minus 5000 is 2x - 5000.

Answer: B

Answer:

B. 2x-5000

Step-by-step explanation:

2x, the 2 means you're going to times that sum by 2. Then you have to subtract 5000 from that which we don't know how much she will have so the equation would be: 2x-5000

The number of hours when Damon and Nicholas will be tied is 2 hours.

The number of hours for the volunteer is 6 hours.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, Damon, who has already completed 2 hours, plans to volunteer for 2 hours per week going forward. Nicholas hasn't started yet, but plans to dedicate 3 hours per week to his volunteer project from now on.

Let the number of hours be h.

Damon's equation will be 2 + 2h

Nicholas equation will be 3h

The number of hours to be tied will be:

2 + 2h = 3h

3h - 2h = 2

h = 2

The number of hours is 2.

The number of hours for the volunteer will be:

= 3h

= 3(2)

= 6 hours.

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The system of equations is:

28cm = 2*(W + L)

28.8cm = 2*(0.9*L + 1.2*W)

b) Solving that we will get L = cm and W = 6cm

c) The figure becomes a square of sides of 7.2cm

First, let's define the variables:

Remember that the perimeter of a rectangle is:

P = 2*(W + L)

We know that the perimeter is 28cm, then:

28cm = 2*(W + L)

And if we decrease the length by 10% and increase the width by 20% the perimeter is 28.8cm, then

28.8cm = 2*(0.9*L + 1.2*W)

Then the system of equations is:

28cm = 2*(W + L)

28.8cm = 2*(0.9*L + 1.2*W)

We can isolate L on the first equation to get:

28cm/2 - W = L

14cm - W = L

Replacing that in the other equation we get:

28.8cm = 2*(0.9*(14cm - W) + 1.2*W)

28.8cm = 1.8*(14cm - W) + 2.4*W

28.8cm = 25.2cm + 0.6*W

28.8cm - 25.2cm =  0.6*W

3.6cm/0.6 = W = 6 cm

So the width is 6cm, then the length is:

L  = 14cm - 6cm = 8cm

c) The modified dimensions are:

0.9*L = 0.9*8cm = 7.2 cm

The new width is:

1.2*W = 1.2*6cm = 7.2 cm

So the length is equal to the width, then the figure becomes a square.

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