find the quotient of 5 divided 1/8

answer:35 grams

explication: because if he need 350 grams of sugar to make 100 cookies , we have to divide 350 by 100 so it gives 35

The number of grams of sugar would he need to bake 10 cookies will be 35 grams.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

To bake 100 of his favorite cookies, Mr.Wallis needs 350 grams of sugar.

Let x be the amount of sugar for 10 cookies.

The number of grams of sugar would he need to bake 10 cookies will be

x / 10 = 350 / 100

x / 10 = 3.5

x = 35 grams

The number of grams of sugar would he need to bake 10 cookies will be 35 grams.

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Answer:

gradient = \(\frac{3}{2}\) , y- intercept = \(\frac{5}{2}\)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

given

2y - 3x = 5 ( add 3x to both sides )

2y = 3x + 5 ( divide through by 2 )

y = \(\frac{3}{2}\) x + \(\frac{5}{2}\) ← in slope- intercept form

with gradient m = \(\frac{3}{2}\) and y- intercept c = \(\frac{5}{2}\)

The gradient is:

The y intercept is:

Work/explanation:

Let's rearrange the equation first so that it's in slope intercept.

Our equation is

\(\bf{2y-3x=5}\)

And we should write it in \(\bf{y=mx+b}\) form. Let's go ahead and perform the required operations.

________________________

Add 3x on each side:

\(\bf{2y=5+3x}\)

\(\bf{2y=3x+5}\)

Now, divide each side by 2:

\(\bf{y=\dfrac{3}{2}x+\dfrac{5}{2}}\)

This is the equation in slope intercept.

As for the gradient, that is the number in front of x : 3/2.

As for the y intercept, that is the constant : 5/2

Hence, these are the answers.

=======================================================

Explanation:

The requirements for a probability distribution are this

Condition #1 shown above allows us to rule out choice C due to -0.10 not being in the interval from 0 to 1.

We can also rule out choice D since the probabilities sum to this

0.20+0.15+0.20+0.20+0.20+0.20 = 1.15

The sum is too large. The sum needs to be 1.00 or just 1.

So that leaves choice A or choice B as the possible answer. Both distributions fit conditions #1 and #2 as shown above (I'll let you confirm these facts). However, choice A is ruled out because that distribution is considered fair. Each probability for choice A is equal, so each side of the cube is equally likely to be landed on.

For choice B, the probabilities are different, so we don't have a fair cube here and it is considered loaded or biased.

Answer:

B is right

Step-by-step explanation:

Guy above me is correct

Answer:

90.3 km

Step-by-step explanation:

2 cm: 21 km and the boss provides 8.6 cm for manhattan-bronx distance.

a ratio can also be written as a fraction

2/21 x 8.6/x  or  2:21 and 8.6:x [cross multiply to solve for x]

2 x 8.6      =     2x = 180.6    =   2x = 180.6  reduces to x =90.3

21    x                                         2         2

The shadow of the tree at the same time of day was 113.29 foot long.

Foot, plural feet, any of numerous ancient, mediaeval, and modern linear measures based on the length of the human foot and used only in English-speaking countries, where it typically consists of 12 inches or one-third yard (typically 25 to 34 cm).

In most countries and all areas of science, the foot and its multiples and subdivisions have been largely replaced by the metre, the basic linear unit of the metric system. Since 1959, a foot in the US has been defined as exactly 30.48 centimetres.

We know that

1 feet = 12 inches

So, 5 feet 8 inches = 5\(\frac{2}{3}\) feet

Now, lets find the shadow of tree

5\(\frac{2}{3}\)/2 = 321/x

x = 113\(\frac{5}{11}\)

x = 113.29

Thus, the tree's shadow at the same time of day was 113.29 foot long

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Answer:

9, 15, 22.

If you add any of the two side lengths, they will be greater than the third.

Step-by-step explanation:

Answer: 2 is the answer

Step-by-step explanation:

When 1,493,600 is divided by 8 the quotient is 186,700.

To divide 1,493,600 by 8, you can follow these steps:

We have to write down the dividend (1,493,600) and the divisor (8).

Now start with the largest place value in the dividend (the leftmost digit) and perform the division.

Divide 1 by 8. Since 1 is smaller than 8, you move to the next digit.

Bring down the next digit (4) and combine it with the previous quotient (0). This gives you 04.

Divide 4 by 8. Since 4 is smaller than 8, you move to the next digit.

Bring down the next digit (9) and combine it with the previous quotient (0). This gives you 09.

Divide 9 by 8. The quotient is 1, and the remainder is 1.

Bring down the next digit (3) and combine it with the remainder (1). This gives you 13.

Divide 13 by 8. The quotient is 1, and the remainder is 5.

Bring down the next digit (6) and combine it with the remainder (5). This gives you 56.

Divide 56 by 8. The quotient is 7, and there is no remainder.

Bring down the next digit (0) and combine it with the quotient (7). This gives you 70.

Divide 70 by 8. The quotient is 8, and there is no remainder.

There are no more digits to bring down, and the division is complete.

The quotient is the result of the division. In this case, 1,493,600 divided by 8 is equal to 186,700.

Therefore, the result of 1,493,600 ÷ 8 is 186,700.

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In order to solve linear equations in two variables two equations are needed. The solution of the equations 2(x + y) = 14 and  y = 11 + x is  x = -2 and y = 9.

A system of linear equations is a group of  equations having same number of variables and degree.

For the n number of variables n number of equations are required.

On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.

Given that,

One of the number is 11 more than the other,

And, twice the sum of two numbers = 14.

Suppose one of the number be x.

And, the other number is y.

Then as per the question the pair of equations can be formed as,

2(x + y) = 14                     (1)

y = 11 + x                        (2)
In order to solve these equations, multiply equation (2) by 2 and then substract it from equation (1) as,

2(x + y) - 2y = 14 - 2(11 + x)

=> 2x = 14 - 22 - 2x

=> 2x + 2x = -8

=> 4x = -8

=> x = -2

Substitute x = -2 in equation (2) to obtain y as,

y = 11 - 2    

y = 9.

Hence, the equations for the given case are 2(x + y) = 14 and  y = 11 + x and their solution is x = -2 and y = 9.

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Answer:

67 math, 142 history

Step-by-step explanation:

lets say the number of math textbooks was x and the number of history textbooks is y. we have x+y=209 and x=y-75. we can plug the second equation into the first to get y-75+y=209. simplfy to get 2y=284 so y=142. since x=y-75, x=67

The completely factorized form of the expression q² - 4 is (q + 2)(q - 2).

Given the expression in the question:

q² - 4

To factorize the expression q² - 4 completely, we can use the formula for the difference of squares.

The difference of squares formula states that :

a² - b² can be factored as (a + b)(a - b).

Given that:

q² - 4

Replace 4 with 2²
q² - 2²

From this expression, let a = x and b = 2

a² - b² =  (a + b)(a - b)

q² - 2² = (q + 2)(q - 2)

Therefore, the factored form is (q + 2)(q - 2).

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The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

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Answer:

4/15

Step-by-step explanation:

2/5 = 6/15

1/3 = 5/15

6/15 + 5/15 = 11/15

15/15 - 11/15 = 4/15

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The ordered pairs for the equation y = -7x + 8 are (0, 8), (1, 1), and (-1, 15).

To find ordered pairs for the equation y = -7x + 8, we can substitute different values of x and solve for y.

Let's choose three values of x:

When x = 0, y = -7(0) + 8 = 8. So one ordered pair is (0, 8).

When x = 1, y = -7(1) + 8 = 1. So another ordered pair is (1, 1).

When x = -1, y = -7(-1) + 8 = 15. So another ordered pair is (-1, 15).

Therefore, the ordered pairs  are (0, 8), (1, 1), and (-1, 15).

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Answer: -5, -9, -26

Step-by-step explanation:

Answer:

The sum of three integers is 38. Two less than 4 times the smaller integer is

equal to the sum of the others. The sum of the smaller and larger integer is

equal to 2 more than twice that of the other.

Step-by-step explanation:

The area of the region enclosed by one loop of the curve r = 3/2 sin(2θ) is 9π/16

How to find the area of and enclosed by equation?

When we need to find the area bounded by a single loop of the polar curve, we use the same formula which was used to find area inside the polar curve in general.

\(A = \int\limits^a_b {1/2 r^2} \, d\theta\\\)

where [a,b] is the interval and r is the given curve equation

According to the given question:

Equation of the given curve is r = 3/2 sin(2θ)

When r = 0, θ = π/2 which corresponds to one loop

Therefore area of the region enclosed by this curve is

A = 9/4 * 1/2 int 0 to π/2 sin²2θ dθ

A = 9/8 int 0 to π/2 (1 - cos4θ)/2 dθ

A = 9/8 * π/2

A = 9π/16

Area of the required loop is 9π/16

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Answer:

a=10/30

Step-by-step explanation:

because you can simplify it to 2/15

Answer:

You cannot add two numbers that have different variables.

Step-by-step explanation:

You can multiply them, but since 3 is multiplied by "a" or a different number than "b" then the answer would be incorrect.

Answer:

because 3a and 3b have different variables. You can't add "unlike terms" to each other because the variables have different values. by writing 3a+2b as 5ab, you're completely changing the meaning of the problem. You would get a totally different answer than you would by just adding the two terms together.

It is Growing Exponential function because the base is greater than 1 and the exponent has a positive sign.

What is exponential decay function?

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

\(y=5^x\)

It is a function called "Exponential function". The base determines the growth or decay of the function.

If  base > 1, then the function grows, otherwise if base is between 0 and 1, the function decays.

Here, the  base is positive and it's not 1 or 0.

If we have

\(y=5^{-x}\)

this function can be rewritten in this way:

\(y=(1/5)^x\)

Here, base between 0 and 1, the function decays

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each case contains 12 paper rolls.

It is given that total number of rolls paper towels is y

and x is the total number of the case,

then y can be represented in term of x

y = 12x

but it is given that 4 rolls are purchased by the customer, we will subtract 4 from total

so now the equation for the total rolls will be,

y = 12x - 4

so it is the equation for total rolls remaining in the store.

And the correct answer is option A.

Answer:

A. 15.31

I did the standard deviation calculator and this is what I got

The confidence interval of the true proportion of low income people who will vote for the introduction of the tax is

Yes, we can conclude that at the 5% level of significance, the proportion of high income voters favoring the new security tax is 10% higher than that of low income voters using Test of Significance for Difference of Proportions.

A confidence interval is the mean of your estimate plus and minus the variation in that estimate.

Proportion of high-income people who will vote for the introduction of the tax = p1 =  \(\frac{80}{100} = \frac{4}{5}\)\(= 0.8\)

Proportion of low-income people who will vote for the introduction of the tax = p2 =  \(\frac{55}{80} = \frac{11}{16}\) \(= 0.6875\)

95% confidence interval of the true proportion of low income people who will vote for the introduction of the tax -

Upper confidence interval -

\(= p + 1.96 \sqrt{pq/n}\)

\(=0.6875 + 1.96 \sqrt{(0.6875)(1-0.6875)/80} \\= 0.6875 + 1.96 \sqrt{0.00268} \\=0.789\)

Lower confidence interval -

\(= p - 1.96 \sqrt{pq/n}\)

\(=0.6875 - 1.96 \sqrt{(0.6875)(1-0.6875)/80} \\= 0.6875 - 1.96 \sqrt{0.00268} \\=0.586\)

Test of Significance for Difference of Proportions is used when we want to compare two distinct populations with respect to the prevalence of a certain attribute, say A, among their members.

n1 = 100

X1 = 80

p1 = 0.8

n2 = 80

X2 = 55

p2 = 0.6875

H0:  the proportion of high-income voters favoring the new security tax is 10% higher than that of low-income voters.(P1 - P2 = 0.1)

H1:  the proportion of high-income voters favoring the new security tax isn't 10% higher than that of low-income voters. (P1 - P2 != 0.1)

\(z = \frac{(p1 - p2) - (P1 -P2)}{(\frac{X1+X2}{n1+n2})(1-\frac{X1+X2}{n1+n2})(\frac{1}{n1}+\frac{1}{n2} ) }\)

\(z = \frac{(0.8 - 0.6875)- 0.1}{\sqrt{0.75*0.25*0.0225} } \\\\z = \frac{0.0125}{0.0649} \\\\z = 0.1926\)

Since z = 0.1926 < 1.96, null hypothesis cannot be rejected. Thus,  the proportion of high-income voters favoring the new security tax is 10% higher than that of low-income voters.

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Answer:

0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860,…

Step-by-step explanation:

Answer:

It will take the two ships at ports M and N 162miles apart 2.33 hours to meet.

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

let the distance both ships meet be x and he time taken to get to x by first ship be t.

second ship: time taken to get to (160 - x) is (t - 0.75) 45 minutes is same as 0.75 hour

so speed of first sheep

45 = x/t

x = 45t--------------1

speed of second ship

36 = 162-x / t - 0.75

cross multiply

36(t - 0.75) = 162 -x

x = 160 - 36(t - 0.75) -------------------2

equate equation 1 and 2

45t = 162 - 36(t - 0.75)

multiply out

45t = 162 -36t + 27

45t+36t = 162+27

81t = 189

t = 189/81

t = 2.33 hours

In conclusion the time taken for both ships to meet is 2.33 hours

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Answer:

Step-by-step explanation:

So in this example we'll be using the difference of squares which essentially states that: \((a-b)(a+b)=a^2-b^2\) or another way to think of it would be: \(a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})\). So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:

\(x^8-16 = (x^4-4)(x^4+4)\)

Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:

\(x^4-4 = (x^2-2)(x^2+2)\)

So completely factored form is: \((x^2-2)(x^2+4)(x^4+4)\)

I'm assuming that's considered completely factored but you can technically factor it further. While the identity difference of squares technically only applies to difference of squares, it can also be used on the sum of squares, but you need to use imaginary numbers. Because \(x^2+4 = x^2-(-4)\). and in this case a=x^2 and b=-4. So rewriting it as the difference of squares becomes: \(x^4+4 = x^4 - (-4) = (x^2-\sqrt{-4})(x^2+\sqrt{-4}) = (x^2-2i)(x^2+2i)\) just something that might be useful in some cases.

We can factor this into \((x^{4}+4)(x^{4} -4)\).

This is because we use  difference of two squares where \(x^{2} -y^{2} = (x+y)(x-y)\)

So we rewrite x^8-16 to x^8-4^2.

This can then be written to the equation I put at the start.

p.s. The reason its \(x^{4}\) is because \(x^{4} * x^{4} = x^{8}\)
(P.S.S I just found that the other helper did it fully so I stopped here, read his, its correct)

Answer: B,E, C

Step-by-step explanation:

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Arcs get their angle measure from the central angle they're in, in this case the central angle of 86°, central to arcED, has a counterpart of a twin vertical angle across the center, since both vertical angles are identical twins that means the central angle for arcAB is 86° also, and that's the arcAB's measure too.