6
Cheryl had 160 stickers more than Gareth. If Cheryl gave 185 stickers
to Gareth, Gareth would have 3 times as many stickers as Cheryl
How many stickers did Gareth have at first?
165​

Answer:

At most 9.12 joules should be required for the bottom 80% of bottled water

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 8.7, \sigma = 0.5[/tex]

How much energy should be required for the bottom 80% of bottled water?

At most the 80th percentile.

The 80th percentile is X when Z has a pvalue of 0.8. So it is X when Z = 0.84.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.84 = \frac{X - 8.7}{0.5}[/tex]

[tex]X - 8.7 = 0.84*0.5[/tex]

[tex]X = 9.12[/tex]

At most 9.12 joules should be required for the bottom 80% of bottled water

Answer:

-7

Step-by-step explanation:

The numerical coefficient of [tex] - 7yz^2 [/tex] is - 7.

The coefficient of -7yz² is -7

In the given equation,

                                  5x⁶÷3xy-7yz²+2y÷z

the coefficient is -7 , because the coefficient is the constant term of an expression.

A numerical coefficient is a constant multiplier of the variable in a term. And here, -7 is preceded by -7yz²

Hence it is the numerical coefficient.

learn more about numerical coefficients:

brainly.com/question/25420238

Answer:  d) 67

Step-by-step explanation:

[tex]determinant\ \left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&j\end{array}\right] = a\cdot det\left[\begin{array}{cc}e&f\\h&j\end{array}\right] -\ b\cdot det\left[\begin{array}{cc}d&f\\g&j\end{array}\right] +\ c\cdot det\left[\begin{array}{cc}d&e\\g&h\end{array}\right][/tex]

[tex]determinant\ \left[\begin{array}{ccc}2&3&4\\-3&2&1\\5&-1&6\end{array}\right] \\\\\\= 2\cdot det\left[\begin{array}{cc}2&1\\-1&6\end{array}\right] -\ 3\cdot det\left[\begin{array}{cc}-3&1\\5&6\end{array}\right] +\ 4\cdot det\left[\begin{array}{cc}-3&2\\5&-1\end{array}\right]\\\\\\=2[2(6)-1(-1)]-3[-3(6)-1(5)]+4[3(-1)-2(5)]\\\\\\=2(13)-3(-23)+4(-7)\\\\\\=26+69-28\\\\\\=\large\boxed{67}[/tex]

Answer:

So if you multiply you get 3*2 square rooted of 2-2*3*7 =

6 square rooted of -40

That is the most simplified I hope

Answer:

[tex]\boxed{\ x=2\ }[/tex]

Step-by-step explanation:

3(10-2x)=18

<=>

10-2x=18/3=6

<=>

2x=10-6=4

<=>

x= 4/2=2

Answer:

Ok, for f(x) = x^2 we have only one x-intercept (actually, two equal x-intercepts) at x = 0.

Now, for g(x) = (x - 2)^2 - 3

First, let's analyze the transformations.

When we have g(x) = f(x - a) this means that we moved "a" units to the right (if a is positive)

When we have g(x) = f(x) + a, this means that (if a > 0) we move the graph "a" units up.

In this case we have both those transformations:

g(x) = f(x - 2) - 3

this means that we move 2 units to the right, and 3 units down (because the number is negative)

now we can find the roots of g(x) as:

g(x) = (x - 2)^2 - 3 = x^2 - 4x  + 4 - 3 = x^2 - 4x + 1 = 0

using the Bhaskara's equation:

[tex]x = \frac{4 +-\sqrt{4^2 - 4*1*1} }{2*1} = \frac{4 +- 3.5}{2}[/tex]

then the roots are:

x = (4 + 3.5)/2 = 3.75

x = (4 - 3.5)/2 = 0.25

Here we have two different x-intercepts

Answer:use mathematic pathway to calualte

Step-by-step explanation:

Answer: 50 student in the school

Step-by-step explanation: 5x10=50 so that’s the answer.

Answer:

D

Step-by-step explanation:

If <CAD=35, <KNL=55 because the remaining angle is 90 since it's a right angle. Therefore <KNM=110 because 55+55=110

Answer:

The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.

Step-by-step explanation:

To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.

The prism and pyramid's bases is 25 cm²

The pyramid's height is 12÷2 or 6 cm

The volume formula for a prism is l×w×h

The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h

The area of the prism is 5×5×12 or 300 cm³

The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³

300 cm³-75 cm³=225 cm³

The volume outside the pyramid but inside the prism is 225 cm³.

Answer:

Step-by-step explanation:

a) The number of students sampled in both populations are large. We can assume that the populations are normally distributed. The populations are also independent.

b) This is a test of 2 independent groups. Let μ1 be the mean responses of students buying lecture notes and μ2 be the mean responses of students not buying lecture notes.

The random variable is μ1 - μ2 = difference in the mean responses of students buying lecture notes and the mean responses of students not buying lecture notes.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 8.48

x2 = 7.8

s1 = 0.94

s2 = 2.99

n1 = 86

n2 = 35

t = (8.48 - 7.8)/√(0.94²/86 + 2.99²/35)

t = 1.32

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [0.94²/86 + 2.99²/35]²/[(1/86 - 1)(0.94²/86)² + (1/35 - 1)(2.99²/35)²] = 0.0706/0.00192021883

df = 37

We would determine the probability value from the t test calculator. It becomes

p value = 0.195

c) Since alpha, 0.01 < than the p value, 0.195, then we would fail to reject the null hypothesis. Therefore, at 5% significance level, the samples do not provide sufficient evidence to conclude that there is a difference in the mean responses of the two groups of the students.

d) The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

For a 99% confidence interval, the z score is 1.2.58. This is determined from the normal distribution table.

x1 - x2 = 8.48 - 7.8 = 0.68

z√(s1²/n1 + s2²/n2) = 2.58√(0.94²/86 + 2.99²/35) = 1.33

The confidence interval is

0.68 ± 1.33

The upper boundary for the confidence interval is

0.68 + 1.01 = 2.01

The lower boundary for the confidence interval is

0.68 - 1.33 = - 0.65

We are confident that the difference in population means responses between the students buying lecture notes and the students not buying lecture notes is between - 0.65 and 2.01

d) For a 95% confidence interval, the z score is 1.96.

z√(s1²/n1 + s2²/n2) = 1.96√(0.94²/86 + 2.99²/35) = 1.01

The confidence interval is

0.68 ± 1.01

The upper boundary for the confidence interval is

0.68 + 1.01 = 1.69

The lower boundary for the confidence interval is

0.68 - 1.01 = - 0.33

Therefore, a 95% confidence interval for (μ1-μ2) would be narrower. This is seen in the values in both scenarios.

Answer:

y=cosx

Step-by-step explanation:

cosx has a domain of all real numbers

Answer:

21

Step-by-step explanation:

Similar triangles. MNL is just ABC but 3/4 the size.

x = 8*3/4 = 6

perimeter woudl be 6+6+9 = 21

Answer:

53.57%

Step-by-step explanation:

We have to calculate first the specific number of events that interest us, if at least 3 are girls, they mean that 2 are boys, therefore we must find the combinations of 3 girls of 5 and 2 boys of 3, and multiply that, so :

# of ways to succeed = 5C3 * 3C2 = 5! / (3! * (5-3)!) * 3! / (2! * (3-2)!)

 = 10 * 3 = 30

That is, there are 30 favorable cases, now we must calculate the total number of options, which would be the combination of 5 people from the group of 8.

# of random groups of 5 = 8C5 = 8! / (5! * (8-5)!) = 56

That is to say, in total there are 56 ways, the probability would be the quotient of these two numbers like this:

P (3 girls and 2 boys) = 30/56 = 0.5357

Which means that the probability is 53.57%

Answer:

Actually, the correct answer for plato users is option D

Step-by-step explanation:

D.  0.821

Answer:

4. 27

Step-by-step explanation:

11-10=1 which is <=16

15-10=5 which is <=16

26-10=16 which is <=16

27-10=17 which isn't <=16

Therefore 27 doesn't satisfy the inequality

Answer:

4.   27

Step-by-step explanation:

w - 10 ≤ 16

w≤16 + 10

w ≤ 26

11 ≤ 26

15≤26

26≤26

26≤ 27 False

Answer:

Graph C is the answer.

Step-by-step explanation:

Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.

Total expenditure is less than $3.

If we represent expense in the equation form then it will be

Expense on pencils + expense on erasers = Total expense which is < 3

0.25X + 0.50Y < 3

Now we divide the inequality by 0.25

X + 2Y < 12

This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.

Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)

Now we come to the graphs. Here dotted line graphs are A or C.

We will calculate the slopes of the lines from the graphs A and C to get tha answer.

For Graph A

The end points are (12, 0) and (0, 3)

So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4

For Graph C.

End points the line are (0, 6) and (12, 0)

Slope of the line = (0-6)/(12-0) = -6/12 = -1/2

Therefore Graph C is the answer.

Answer:

Graph C is the answer.

Step-by-step explanation:

Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.

Total expenditure is less than $3.

If we represent expense in the equation form then it will be

Expense on pencils + expense on erasers = Total expense which is < 3

0.25X + 0.50Y < 3

Now we divide the inequality by 0.25

X + 2Y < 12

This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.

Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)

Now we come to the graphs. Here dotted line graphs are A or C.

We will calculate the slopes of the lines from the graphs A and C to get tha answer.

For Graph A

The end points are (12, 0) and (0, 3)

So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4

For Graph C.

End points the line are (0, 6) and (12, 0)

Slope of the line = (0-6)/(12-0) = -6/12 = -1/2

Therefore Graph C is the answer.

Step-by-step explanation:

make brainiest please

Answer:

L = 3/4

Option A. The Root Test says that the series converges absolutely.

Step-by-step explanation:

By using the root test equation given in the question. L = 3/4

Since L < 1, the series converges absolutely.

For clarity of expression, the detailed calculation is contained in the attached file. Check the file attached for the complete calculation to this question.

Functions

Vertical Line Test

Let's see what we are given.

We are given a graph of an inverse of a function.

We need to figure out whether the graphed inverse function is a function or not.

By the definition of a function, we know that every x input must correlate with one y output. In layman's terms, each respective x input has its own specific y output.

This definition builds the foundation of the Vertical Line Test. We can use this simple "tool" to verify whether or not a given graph is a function or not.

When we apply the Vertical Line Test to the graphed inverse function, we can see that every x input has only one specific y output.

∴ we can conclude that the graphed inverse function is indeed a function.

The answer to the question would be A. True.

___

Learn more about functions: https://brainly.com/question/30017262

Learn more about Algebra I: https://brainly.com/question/17011730

___

Topic: Algebra I

Unit: Functions

Answer:

the area of the circle is 102.11 square metres

Answer:

1651

Step-by-step explanation:

let s say that the price before the increase is x

to apply an increase of 9% it does x + x*0.09 = x*(1+0.09)=x*1.09

and we know that this value is 1800

so

x*1.09=1800

<=>

x = 1800/1.09=1651.376147

to the nearest penny it gives 1651

Answer:

Hello!

Answer: 1651

I hope that was correct.  Please let me know, thank you!

Step-by-step explanation:

Answer:

  $140

Step-by-step explanation:

You can add up the prices to find the total. Most of us find it easier to multiply the price by the number of items.

  cost of 2 shirts = (2)($25.00) = $50

  cost of 4 pants = (4)(22.50) = $90

The total was $50 +90 = $140.

Answer:

9.222222222

Step-by-step explanation:

7+21+2+17+3+13+7+4+9 = 83

7+21+2+17+3+13+7+4+9 = 83 83÷9 = 9.222222222

_____________________________

Hey!!

Solution,

Given data=7,21,2,17,3,13,7,4,9

summation FX= 83

N(total no. of items)=9

Now,

Mean=summation FX/N

= 83/9

=9.23

So the answer is 9.23

__________________________

Answer:  see boxed answers below

Step-by-step explanation:

(i) multiply the exponent to the coefficient then subtract 1 from the exponent.

[tex]y=\dfrac{3}{5x^3}+3x^4+2x^2-20\\\\\\\text{rewrite it as follows}: y=\dfrac{3}{5}x^{-3}+3x^4+2x^2-20x^0\\\\\\y'=(-3)\dfrac{3}{5}x^{-3-1}+(4)3x^{4-1}+(2)2x^{2-1}-(0)20x^{0-1}\\\\\\y'=-\dfrac{9}{5}x^{-4}+12x^3+4x^1-0\\\\\\y'=\large\boxed{-\dfrac{9}{5x^{4}}+12x^3+4x}[/tex]

(ii) Use the division formula:    [tex]y = \dfrac{a}{b}\rightarrow \quad y'=\dfrac{ab'-a'b}{b^2}[/tex]

[tex]a=5x^3+1\qquad \qquad a'=15x^2\\b=3x^5+4x^2\qquad \quad b'=15x^4+8x\\\\\\y'=\dfrac{(15x^2)(3x^5+4x^2)-(5x^3+1)(15x^4+8x)}{(3x^5+4x^2)^2}\\\\\\.\quad =\dfrac{45x^7+60x^4-75x^7-55x^4-8x}{(3x^5+4x^2)^2}\\\\\\.\quad =\large\boxed{\dfrac{-35x^7+5x^4-8x}{(3x^5+4x^2)^2}}[/tex]

Answer:

y=2.4

Step-by-step explanation:

7y-2=2y+10

7y-2y=10+2

5y=12

y=12/5=2.4

Answer:

6.68% probability that the mean weight is below 68.5g.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]

Probability that the mean weight is below 68.5g:

This is 1 subtracted by the pvalue of Z when X = 68.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{68.5 - 70}{1}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

6.68% probability that the mean weight is below 68.5g.

Answer:

P(x ∠ 68.5) = 0.07

Step-by-step explanation:

Got it right on khan.

Work Shown:

v - w = ( v ) - ( w )

v - w = ( -3i ) - ( 2-4i)

v - w = ( 0-3i ) - ( 2-4i)

v - w = 0-3i   -2+4i

v - w = (0-2) + (-3i+4i)

v - w = -2 + i

Answer:

He earns $2,100 in two weeks.

Step-by-step explanation:

We know that this street performers earn $60 per day at the Barclays center subway station, and that this earning represents 40% (or a proportion of 0.4) of his daily earnings. We can calculate his daily earnings as:

[tex]0.4D=\$\,60\\\\D=\dfrac{\$\,60}{0.4}=\$\,150[/tex]

If the daily earnings are $150, the earnings in 2 weeks (14 days) will be:

[tex]W=14\cdot\$\,150=\$\,2100[/tex]

Answer:

The correct answer to the following question will be Option A (67.9%).

Step-by-step explanation:

As we know,

The number of total employees will be:

= 480

The number of employees having normal or low BP will be:

= 96 + 230

= 326

Hence, the percentage of low or normal BP workers will be:

= [tex](\frac{326}{480} )\times 100 \ percent[/tex]

= [tex]67.9 \ percent[/tex]

Note:- % (percent)

Answer:

76

Step-by-step explanation:

The two angles are vertical angles so they are equal

3x+7 = 4x-16

Subtract 3x from each side

3x-3x+7 = 4x-3x-16

7 = x-16

Add 16 to each side

7+16 = x-16+16

23 =x

We want YAX

YAX = 3x+7

3*23+7

69+7

76

Answer:

P(B) = 0.62

Step-by-step explanation:

P(A or B) = P(A) + P(B) - P(A and B)

So, Putting the givens

0.89 = 0.48 + P(B) - 0.21

0.89 = 0.27 + P(B)

P(B) = 0.89 - 0.27

P(B) = 0.62