Melanie has D dimes and Q quarters. She has no less than $4 worth of coins altogether. Write this situation as an inequality.

Answer:

[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]

Step-by-step explanation:

We need to find 9 rational number between [tex]\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}[/tex]

We make the denominators of both fractions same. So,

[tex]\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}[/tex]

and

[tex]\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}[/tex]

The rational number are:

[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]

Answer: 3 years

Step-by-step explanation:

Interest is calculated as:

= (P × R × T) / 100

where

P = principal = 150,000

R = rate = 2.5%.

I = interest = 11250

T = time = unknown.

I = (P × R × T) / 100

11250 = (150000 × 2.5 × T)/100

Cross multiply

1125000 = 375000T

T = 1125000/375000

T = 3

The time taken will be 3 years

The answer is 36 degrees

Step 1

Angle GEH=180-2x (angles on a a straight line are supplementary)

Step 2

4x= G^+GE^H(sum of exterior angle)

4x=x+(180-2x)

4x=180-x

4x+x=180

5x=180

x=36 degrees

Answer:

SAS=side angle side

there is two side and one angle

Answer:

SAS theorem

explanation:

Answer:

[tex]Var = 1.9[/tex]

Step-by-step explanation:

Given

[tex]p = \frac{1}{20}[/tex]  i.e. 1 per 20cc of water

[tex]n = 40[/tex] -- sample size

Required

The variance

This is calculated using:

[tex]Var = np(1 - p)[/tex]

So, we have:

[tex]Var = 40 * \frac{1}{20} * (1 - \frac{1}{20})[/tex]

[tex]Var = 40 * \frac{1}{20} * \frac{19}{20}[/tex]

[tex]Var = 2 * \frac{19}{20}[/tex]

[tex]Var = \frac{38}{20}[/tex]

[tex]Var = 1.9[/tex]

Answer:

[tex]{ \tt{2x + 4y = 8 - - - (a)}} \\ { \tt{x = 3y - 6 - - - (b)}} [/tex]

Substitute for x in equation (a) :

[tex]{ \tt{2(3y - 6) + 4y = 8}} \\ { \tt{6y - 12 + 4y = 8}} \\ { \tt{10y = 20}} \\ y = 2[/tex]

Substitute for y in equation (b) :

[tex]{ \tt{x = (3 \times 2) - 6}} \\ x = 0[/tex]

2x+4y =8

x=3y-6 ——> x–3y=–6

x–3y = – 6 ] ×(–2) ——> –2x +6y=12

2x+4y=8

–2x+6y =12

__o_o____

0+10y=20 —> 10y= 20 —> y= 20/10 —> y= 2

2x+4y=8 —> 2x + 4(2) = 8 —> 2x + 8=8 —> 2x = 0 —> x=0

(x,y) —> (0,2)

Answer:

p and q are two numbers.whrite down an expression of

Answer:

answer

x = -13/ 15, 0

Step-by-step explanation:

15x^2 + 13 x = 0

or, x(15x + 13) = 0

either, x = 0

or, 15x + 13 = 0

x = -13/15

Answer:

The answer should be C...............

imma sorry if I'm wrong

Answer:

Answer = √(0.301 × 0.699 / 83) ≈ 0.050

A 68 percent confidence interval for the proportion of persons who work less than 40 hours per week is (0.251, 0.351), or equivalently (25.1%, 35.1%)

Step-by-step explanation:

√(0.301 × 0.699 / 83) ≈ 0.050

We have a large sample size of n = 83 respondents. Let p be the true proportion of persons who work less than 40 hours per week. A point estimate of p is  because about 30.1 percent of the sample work less than 40 hours per week. We can estimate the standard deviation of  as . A  confidence interval is given by , then, a 68% confidence interval is , i.e., , i.e., (0.251, 0.351).  is the value that satisfies that there is an area of 0.16 above this and under the standard normal curve.The standard error for a proportion is √(pq/n), where q=1−p.

Hope this answer helps you :)

Have a great day

Mark brainliest

The line in the middle is half the length of the line on the outside. Multiply the middle line by 2 and set it equal to the outside line.

2(x-3) = x + 6

Simplify:

2x -6 p x + 6

Add 6 to both sides

2x = x + 12

Subtract x from both sides:

X = 12

The answer is B) 12

Answer:

we conclude that population mean is not 11.5

Step-by-step explanation:

The hypothesis :

H0 : μ = 11.5

H1 : μ ≠ 11.5

The test statistic :

(xbar - μ) ÷ (s/√(n))

Test statistic = (12 - 11.5) ÷ (2/√(16))

Test statistic = (0.5) ÷ (2 ÷ 4)

Test statistic = 0.5 / 0.5

Test statistic = 1

The Pvalue from test statistic value, df = n - 1 = 16 - 1 = 15

Pvalue = 0.333

Pvalue > α ; we fail to reject the null ; Hence, we conclude that population mean is not 11.5

Answer:

18

Step-by-step explanation:

Supplementary angles means sum of angles is 180.

4x + 4 + 6x - 4 = 180

4x + 6x + 4 - 4 = 180

10x = 180

x = 180 / 10

x = 18

Answer:

x=18 degree

Step-by-step explanation:

If they are supplementary angles, then their sum = 180 degree

4x+4 + 6x-4 =180

4x+6x + 4-4 = 180

10x = 180

x=180/10

x=18

Answer:

The total distance Allie traveled was 0.81 miles.

Step-by-step explanation:

Since Allie rode her bike up a hill at an average speed of 12 feet / second, and she then rode back down the hill at an average speed of 60 feet / second, and the entire trip took her 2 minutes, to determine what is the total distance she traveled, the following calculation must be performed:

12 + 60 = 72

72 x 60 = 4320

1000 feet = 0.189394 miles

4320 feet = 0.8181818 miles

Therefore, the total distance Allie traveled was 0.81 miles.

Answer:

A. 754 cm²

Step-by-step explanation:

Amount of cardboard needed = surface area of the cone

Curved surface area of the cone = πrl

Where,

π = 3.14

r = ½(20) = 10 cm

l = 24 cm

Plug in the values into the formula

Curved surface area = 3.14 × 10 × 24 = 753.6 ≈ 754 cm²

Step-by-step explanation:

let y = x+5/4

Interchanging x and y , we get ;

x = y+5/4

or, 4x = y+5

or, 4x-5 = y

or, g(x) -1 = 4x-5

Answer:

In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:

4x-5

Answer:

Solution given:

B.g(x)=[tex]\frac{x+5}{4}[/tex]

let

g(x)=y

y=[tex]\frac{x+5}{4}[/tex]

Interchanging role of x and y

we get:

x=[tex]\frac{y+5}{4}[/tex]

doing crisscrossed multiplication

4x=y+5

y=4x-5

So

g-¹(x)=4x-5

Answer:

Bunny Hill Ski Resort:

y = 10x + 35

Diamond Ski Resort:

y = 5x + 40

Point where the cost is the same:

(1, 45)

Step-by-step explanation:

The question tells us that:

$35 and $40 are initial fees

$10 and $5 are hourly fees

This means that x and y will equal:

x = number of hours

y = total cost of ski rental after a number of hours

So we can form these 2 equations:

y = 10x + 35

y = 5x + 40

Now we are going to use System of Equations to find what point the cost of both ski slopes is the same.

Because they both equal y, we can set the equations equal to each other:

10x + 35 = 5x + 40

And we use basic algebra to solve for x:

10x + 35 = 5x + 40

(subtract 5x from both sides)

5x + 35 = 40

(subtract 35 from both sides)

5x = 5

(divide both sides by 5)

x = 1

Remember, x equals the number of hours.

That means when your rent out the skis for 1 hour, you will get the same price of $45 (you find the price by plugging in 1 into both of the equations)

Hope it helps (●'◡'●)

Answer:

A FORMULA is an expression that uses variables to state a rule.

Answer: 10

Step-by-step explanation:

4 x 2 x 5 = 40

9 + 2 + 7 + 8 + 4 = 30

40 - 30 = 10

= 10

Answer:

The empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 62, standard deviation of 8.

What is the approximate percentage of trees planted between 38 and 86?

38 = 62 - 3*8

86 = 62 + 3*8

So within 3 standard deviations of the mean, which, by the empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.

Answer:

[tex](a)\ P(White) = \frac{1}{2}[/tex]

(b) 10 additional white balls

(c) 10 additional black balls

Step-by-step explanation:

Given

[tex]White = 5[/tex]

[tex]Black =3[/tex]

[tex]Red = 2[/tex]

Solving (a): P(White)

This is calculated as:

[tex]P(White) = \frac{White}{Total}[/tex]

[tex]P(White) = \frac{5}{5+3+2}[/tex]

[tex]P(White) = \frac{5}{10}[/tex]

[tex]P(White) = \frac{1}{2}[/tex]

Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]

Let the additional white balls be x

So:

[tex]P(White) = \frac{White+x}{Total+x}[/tex]

This gives:

[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]

Cross multiply

[tex]30+3x = 20 + 4x[/tex]

Collect like terms

[tex]4x - 3x = 30 - 20[/tex]

[tex]x = 10[/tex]

Hence, 10 additional white balls must be added

Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]

Let the additional black balls be x

So:

[tex]P(White) = \frac{White}{Total+x}[/tex]

So, we have:

[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]

Cross multiply

[tex]10+x = 5 * 4[/tex]

[tex]10+x = 20[/tex]

Collect like terms

[tex]x = 20 -10[/tex]

[tex]x = 10[/tex]

Hence, 10 additional black balls must be added

Answer: 1, 4

Step-by-step explanation:

[tex]\frac{1}{4} x+x=5\\\\\frac{1}{4} x+\frac{4}{4} x=5\\\\\frac{5}{4} x=5\\\\5x=4*5\\5x=20\\x=4[/tex]

Answer:

The choose (A)

y=(x-1)²-2

Answer:

i put in 3 to make 23436 because 36 is divisible by 6

9514 1404 393

Answer:

  (c)

Step-by-step explanation:

  [tex]\displaystyle\sqrt[3]{xy^5}\sqrt[3]{x^7y^{17}}=\sqrt[3]{x^{1+7}y^{5+17}}=\sqrt[3]{x^6x^2y^{21}y}=\sqrt[3]{x^6y^{21}}\sqrt[3]{x^2y}\\\\=\boxed{x^2y^7\sqrt[3]{x^2y}}[/tex]

Answer:

12x^3 is equivalent to

12x*12x*12x which if we multiply is

1728x

we divide by 4x

1728x divided by 4x=432x

Hope This Helps!!!

Answer:

3x^2

Step-by-step explanation:

when u divide 12x^3/4x....u divide 12/4=3 along with the x also..tat is x^3/x=x^2

Answer:

Metro and Medec

METRO

Post-merger Financial Position, using the pooling of interest method:

Pre-merger Financial Positions:

                           Metro (RM ‘000)

Assets  

Current assets                          120

Fixed assets                             830

Total assets                             950

Liabilities and Equities  

Current liabilities                      40

Long term debt                      200

Common stock (RM1 par)      480

Capital surplus                       120

Retained earnings                  110

Total liabilities and equity    950

Earnings available to

common stockholders            230

Common Dividends                  150

Addition to Retained Earnings  80

Step-by-step explanation:

Pre-merger Financial Positions:

                           Metro (RM ‘000)    Medec(RM ‘000)

Assets  

Current assets                          50                     70

Fixed assets                           650                    180

Total assets                            700                   250

Liabilities and Equities  

Current liabilities                      30                     10

Long term debt                       140                    60

Common stock (RM1 par)      400                    80

Capital surplus                         50                    70

Retained earnings                   80                    30

Total liabilities and equity     700                 250

Earnings available to

common stockholders            100                  130

Common Dividends                  50                  100

Addition to Retained Earnings 50                   30

Exchange ratio = 1:2

Pentagon has sum of 540°

Answer:

A. 8x = amount of broccoli needed

B. 4 people; 32÷8=4

Step-by-step explanation:

A. the variable (x) represents the amount of people.

B. 32 ounces divided by 8 ounces is enough for four people.

Answer:

0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%

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 normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose 46% of politicians are lawyers.

This means that [tex]p = 0.46[/tex]

Sample of size 662

This means that [tex]n = 662[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.46[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.46*0.54}{662}} = 0.0194[/tex]

What is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%?

p-value of Z when X = 0.46 + 0.04 = 0.5 subtracted by the p-value of Z when X = 0.46 - 0.04 = 0.42. So

X = 0.5

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.5 - 0.46}{0.0194}[/tex]

[tex]Z = 2.06[/tex]

[tex]Z = 2.06[/tex] has a p-value of 0.9803

X = 0.42

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

[tex]Z = \frac{0.42 - 0.46}{0.0194}[/tex]

[tex]Z = -2.06[/tex]

[tex]Z = -2.06[/tex] has a p-value of 0.0197

0.9803 - 0.0197 = 0.9606

0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%