- A jar contains 55 quarters and dimes. The total value of the coins is $8.50. Find the
number of quarters and dimes in the jar.

IfIf AD BD, the following relationships that can be proved and why is: D. ΔACD ΔBCD, because of SAS.

The relationship that can be proved is ΔACD ΔBCD, because of SAS.

The reason is that m<CDA=M<CDB=90°

CD=CD

AD=BD

Hence, ΔACD=ΔBCD because of SAS. SAS congruence can tend to be proved when the length of the two side correspond and when  the angle between the two side is equal.

Therefore the correct option is D.

Learn more about Relationship that can be proved if AD=BD here:https://brainly.com/question/16906407

#SPJ1

Answer:

the slope is -7

Step-by-step explanation:

\(\frac{-2-5}{3-2} =\frac{-7}{1}\)

Answer:

y = -1/3x - 11/3

Step-by-step explanation:

line a: y = -1/3x - 5

3 = -1/3(2) - b

3 = -2/3 - b

3 + 2/3 = b

3/1 + 2/3 = b

9/3 + 2/3 = b

11/3 = b

Louise has 132 points after hitting the blue target first, then the red target.

Adam also has 132 points after hitting the red target first, then the blue target.

Louise hits the blue target first, then the red target:

Starting score: 100 points

Hitting the blue target increases the score by 10%

100 + (10/100) × 100

= 100 + 10

= 110 points

Hitting the red target increases the score by 20%:

110 + (20/100) × 110 = 110 + 22 = 132 points

b) Adam hits the red target first, then the blue target:

Starting score: 100 points

Hitting the red target increases the score by 20%: 100 + (20/100) × 100 = 100 + 20 = 120 points

Hitting the blue target increases the score by 10%: 120 + (10/100) × 120 = 120 + 12 = 132 points

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ1

Answer:132 each

Step-by-step explanation:

The probabilities are (a) 0.948 and (b) 1.04.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

Given that,

Total number of drivers = 97 drivers

Out of those 97 drivers, 36 were men who were ticketed, 12 were men who were not ticketed, 8 were women who were ticketed, and 41 were women who were not ticketed.

Probability of getting a man who was ticketed = 36/97

Probability of getting a man who was not ticketed = 12/97

Probability of men = 36/97 + 12/97 = 48/97

Probability of getting a woman who was ticketed = 8/97

Probability of getting a woman who was not ticketed = 41/97

Probability of women = 8/97 + 41/97 = 49/97

(a)  Probability that the selected person is a man or someone who was ticketed = P(man) + P(someone who was ticketed)

              = 48/97 + (36/97 + 8/97)

              = 48/97 + 44/97

              = 92/97 = 0.948

(b) Probability that the selected person is a man or someone who was not ticketed = P(man) + P(someone who was not ticketed)

                    = 48/97 + (12/97 + 41/97)

                    = 48/97 + 53/97

                    = 101/97 = 1.04

Hence the probabilities are 0.948 and 1.04.

Learn more about Probabilities here :

https://brainly.com/question/30034780

#SPJ1

Answer:

Fahad is taller with 31 centimeters

Step-by-step explanation:

1090mm=109cm

Fahad is taller than Fareed by 31 centimeters.

1090 mm = 109 cm

140 cm - 109 cm = 31 cm

Hope this helps; please mark brainliest!

Have an amazing day!

Answer:

2) 70,000

Step-by-step explanation:

since they have said estimate meaning frist round off

679 rounds up to 700 and 98 rounds up to 100

700×100

70000

how will his speed compare?  or namely, will he be within speed limits or should we give him a big fat ticket for speeding?

well, the 25 mi/hr limit is expecting anyone on that road to only do 40,234 meters per hour, so since an hour is 60 minutes and a minute is 60 seconds, that means an hour is really (60)(60) seconds, or 3600 seconds, so the limit is expecting anyone on that road to do no more than 40,234 meters per 3600 seconds, let's see how Usain fares

\(\begin{array}{ccll} meters&seconds\\ \cline{1-2} 100 & 9.63\\ 40234& x \end{array} \implies \cfrac{100}{40234}~~=~~\cfrac{9.63}{x} \implies 100x=(40234)(9.63) \\\\\\ x=\cfrac{(40234)(9.63)}{100}\implies x\approx 3874.53\)

so Usain will covering those 40,234 meters in about 3875 seconds, that's longer than 3600 seconds, meaning Usain will need more than 3600 seconds to cover those meters so he's really going slower 40,234 meters per 3600 seconds, so he's golden,  he's within speed limits, because the limit is expecting noone to do them in less than 3600 seconds.

To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

To learn more about equal variances: -brainly.com/question/30777199

#SPJ11

To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

To learn more about equal variances: -brainly.com/question/30777199

#SPJ11

The distance he will drive with 5 gallons of gas is 165 miles

The given parameters are

264 miles = 8 gallons of gas

For 5 gallons of gas, we have

x = 5 gallons of gas

So, we have the following equations

264 miles = 8 gallons of gas

x = 5 gallons of gas

Next, we multiply both sides of the above equations

This gives

8 * x = 264 * 5

Evaluate the products

So, we have

8x = 1320

Divide both sides of the equation by 8

So, we have

x = 165

Hence, the distance he will drive with 5 gallons of gas is 165 miles

Read more about distance at

https://brainly.com/question/14335655

#SPJ1

An equation of the form \(x^2 + bx + c = 0\) that has the solutions x = -4 and x = 6 can be obtained by expanding the equation (x - (-4))(x - 6) = 0. This simplifies to \(x^2 - 2x - 24 = 0.\)

To find an equation of the form \(x^2 + bx + c = 0\) with the given solutions x = -4 and x = 6, we can start by using the fact that the product of the roots of a quadratic equation is equal to the constant term divided by the coefficient of \(x^2\). In this case, the product of the roots is (-4) * 6 = -24.

We can then write the equation as (x - r1)(x - r2) = 0, where r1 and r2 are the roots. Substituting the given values, we have (x - (-4))(x - 6) = 0. Expanding this equation gives \(x^2 - 2x - 24 = 0.\)

Therefore, the equation\(x^2 - 2x - 24 = 0\) has the solutions x = -4 and x = 6. This equation satisfies the form \(x^2 + bx + c = 0\), where b = -2 and c = -24. By rearranging the terms, we can easily identify the coefficients b and c in the equation.

Learn more about quadratic here:

https://brainly.com/question/22364785

#SPJ11

Step-by-step explanation:

Equation 1

\(\frac{m^2}{6} -\frac{9}{4m}\\\\ by\ taking\ LCM\\\\ \frac{2m^3-27}{12m}\)

Equation 2

\(\frac{x^3}{w} -\frac{2}{wx^2}\\\\ by\ taking\ LCM\\\\ \frac{x^5-2}{wx^2}\)

Solution

To write r > -10/3 on a number line,

Step 1: Draw a number line and include -10/3 on it

Step 2: Draw an arrow to the right with the small circle at its initial

The formula for the area of the rectangle, A, in terms of the length, L, is given by A(L) = L(10 - L) square meters. The domain of A is the set of all possible values for L, which in this case is the interval [0, 10].

To find the formula for the area, we start by noting that the perimeter of the rectangle is 20 m. Since the perimeter is the sum of all sides, we can express it as follows:

Perimeter = 2(length + width) = 20.

Since the length of the rectangle is longer than its width, we can assume that L represents the length and (10 - L) represents the width. Rearranging the equation for the perimeter, we have:

2(L + (10 - L)) = 20,

2(10) = 20,

20 = 20.

This equation holds true, confirming that the length L and the width (10 - L) satisfy the given conditions. Finally, the area A is given by the product of the length and width:

A(L) = L(10 - L) square meters.

The domain of A is determined by the range of possible values for L, which in this case is [0, 10]. Since the length of a side cannot be negative or exceed 10, the domain of A is the interval [0, 10].

Learn more about perimeter here:

https://brainly.com/question/7486523

#SPJ11

Therefore, there are 8^13 ways for Felicity to make her candy bar selection at the grocery store.

To calculate the number of ways Felicity can make her selection, we need to consider that she can choose from the available varieties of candy bars. Since there are 8 varieties in total, she has 8 options for the first candy bar. Similarly, for the second candy bar, she still has 8 options since she can choose from the same varieties again. This process continues for all 13 candy bars.

To find the total number of ways, we multiply the number of options for each candy bar together. Since each candy bar is chosen independently, the total number of ways Felicity can make her selection is calculated as 8 multiplied by itself 13 times (8^13). This yields a large number of possible combinations, representing the various ways she can choose candy bars from the available varieties.

Learn more about number here:

https://brainly.com/question/3589540

#SPJ11

Jeffrey has a fish tank that holds 8 liters of water. He already has the tank filled with 1 liter of water. Thus, to fill the fish tank completely with water, Jeffrey needs 7000 milliliters of water.

This is because 1 liter is equal to 1000 milliliters. Thus, 8 liters are equal to 8 × 1000 = 8000 milliliters.

Therefore, the amount of water Jeffrey needs to completely fill the fish tank is 8000 - 1000 = 7000 milliliters of water.

Jeffrey has a fish tank of 8 liters of water that already has 1 liter of water in it.

The amount of water Jeffrey needs to completely fill the fish tank is calculated by subtracting the liters of water already present in the tank from the total liters of water the tank can hold.To completely fill the fish tank, Jeffrey needs to fill the remaining 7 liters with water. One liter of water is equivalent to 1000 milliliters. Thus, Jeffrey needs to multiply the remaining liters of water he needs to fill by 1000 milliliters.

7 × 1000 = 7000

Therefore, Jeffrey needs 7000 milliliters of water to completely fill the fish tank with water.

To completely fill the fish tank, Jeffrey needs 7000 milliliters of water because he has already filled it with 1 liter of water, and the fish tank can hold 8 liters of water.

To know more about fish tank visit:

brainly.com/question/3381308?

#SPJ11

The formula y=58249e - 0.05x is an exponential decay function commonly used to model the decay of biological material or the growth of bacterial cultures over time. The value of y represents the initial value or quantity at time zero, and x represents the time elapsed since the initial value. The constant e is the base of the natural logarithm, and the coefficient -0.05 represents the decay rate per unit of time.

The formula y=58249e - 0.05x is an exponential decay function commonly used in various fields including biology, physics, and finance. In this formula, y represents the initial value or quantity at time zero, and x represents the time elapsed since the initial value.

The constant e (approximately equal to 2.718) is the base of the natural logarithm, and the coefficient -0.05 represents the decay rate per unit of time. As time increases, the value of y decreases exponentially.

In biology, this formula can be used to model the decay of biological material or the growth of bacterial cultures over time.

The decay rate represents the rate at which the biological material or culture is breaking down or dying off, and the initial value represents the starting amount of material or the size of the culture at time zero.

Visit here to learn more about coefficient:

brainly.com/question/1038771

#SPJ11

If joe walks by 21 cats in one week then 7 cats are black.

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

For Example , 1%= 1/100

Given that Joe's town there are 33 black cats

Total cats = 100.

The percentage of black cats in town =\(\frac{33}{100}\)=33%

Number of cats joe sees in a week =21

Number of black cats joe sees in a week will be = 33% of 21

\(=21*\frac{33}{100} \\ \\ =\frac{693}{100} \\ \\ =6.93\\ \\\)= approx. 7

Therefore , If joe walks by 21 cats in one week then 7 cats are black.

Learn more about Percentage here https://brainly.com/question/14801224

#SPJ4

Answer:

a. Income = $408.75

b. Income = $300 + $0.05x

Step-by-step explanation:

Given

Salary = $300 weekly

Commission = 5% of total sales

Solving (a): When total sales = $2175

To calculate his total income, we make use of...

Income = Salary + 5% * Total Sales

\(Income = \$300 + 5\% * \$2175\)

\(Income = \$300 + \$108.75\)

\(Income = \$408.75\)

Solving (b): When total sales = $x

Income = Salary + 5% * Total Sales

\(Income = \$300 + 5\% * \$x\)

Convert % to decimal

\(Income = \$300 + 0.05 * \$x\)

\(Income = \$300 + \$0.05x\)

Answer:

Exact Form:

\(\frac{28}{3}\)

Decimal Form:

9.3¯ (where the three is repeating)

Mixed Number Form:

\(9\frac{1}{3}\)

The simplified expression are as follows;

6mn³ - mn² +  3mn³ + 15mn² =  9mn³ + 14mn²

a⁴b³ + 8a⁴b³  = 9a⁴b³

A simplified expression is express to its lowest term.

Therefore,

6mn³ - mn² +  3mn³ + 15mn²

combine like terms

6mn³  +  3mn³ - mn² + 15mn²

9mn³ + 14mn²

a⁴b³ + 8a⁴b³  = 9a⁴b³

learn more on simplification here: https://brainly.com/question/403991

#SPJ1

The values of function g(x) are as follows:

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

Given, a relation between two functions in terms of variables

      the value of g(x) = x* f(x) = -2 *1 = -2

      the value of g(x) = x* f(x) = 0 *-2 = 0

      the value of g(x) = x* f(x) = 1 *-5 = -5

      the value of g(x) = x* f(x) = 3 *-4 = -12

Therefore, The values of the given function are -2, 0, -5, and -12.

Learn more about function here:

https://brainly.com/question/29120892

#SPJ1

Complete question:

g(x) = x f(x)

Answer:

0.9082

Step-by-step explanation:

z=(63-67)/3=-1.3333

using a calculator we can find the probability is 0.9082 rounded to four decimal places

Answer:

8 / 29 = .276

Step-by-step explanation:

29 is the total number of jelly beans

When we have replacement, we do not reduce the number of total jelly beans, so the probably of drawing blue stays the same.

Answer:

.276

Step-by-step explanation:

Answer:

When x = 0, then y = -2

When y = 0, then x = 4

Step-by-step explanation:

We are given with the following equation;

x - 2y = 4

Now, we have to find the respective values of x and y for each value of x = 0 and y = 0.

Firstly, putting the value of x = 0;

x - 2y = 4

0 - 2y = 4

-2y = 4

y = \(\frac{4}{-2}\)  = -2

This means that when x = 0, then y = -2.

Similarly, putting the value of y = 0;

x - 2y = 4

\(x-(2\times 0)=4\)

x - 0 = 4

x = 4

This means that when y = 0, then x = 4.

The change in the nominal exchange rate, in Canada's perspective, is a depreciation of the Canadian dollar by 2.76%.

Nominal exchange rate is the price of one currency in terms of another currency. It represents the number of units of one currency that can be purchased with a single unit of another currency. In Canada's perspective, a change in nominal exchange rate means the value of the Canadian dollar in US dollars. So, to calculate the change in nominal exchange rate from Canada's perspective.

Nominal Exchange Rate = Real Exchange Rate x (1 + Inflation of Canada) / (1 + Inflation of US) Given, Real Exchange Rate of Canada

= 4.9% Inflation of Canada

= 8.5% Inflation of US

= 3.8%  Nominal Exchange Rate

= 4.9% x (1 + 8.5%) / (1 + 3.8%) Nominal Exchange Rate

= 4.9% x 1.085 / 1.038 Nominal Exchange Rate

= 5.3099 / 1.038 Nominal Exchange Rate

= 5.11 (rounded to two decimal places)

This means that if there were no inflation, the nominal exchange rate from Canada's perspective would have been 5.11 Canadian dollars per US dollar. But due to inflation, the Canadian dollar depreciated by 2.76% (calculated as (5.11 - 4.97) / 5.11 x 100%). Therefore, the change in the nominal exchange rate, in Canada's perspective, is a depreciation of the Canadian dollar by 2.76%.

To know more about nominal, visit:

https://brainly.com/question/27994820

#SPJ11

Measure of arc MLK is 270°

Angle MKL = 135 degrees

We are looking for the measure of the arc MLK

The diagram shows an angle formed by a chord (MK) and tangent

The relationship between angle formed by a chord and tangent:

Measure of arc MLK:

Answer:

Step-by-step explanation:

The compound interest formula is expressed as \(A = P(1+r/n)^{nt}\)

A is the total amount after n years

P is the amount deposited (principal)

r is the rate (in %)

t is the time (in years)

n is the time of compounding

Given P =  $5000, r = 4% = 0.04, t = 5 years, n = 1 year (per annum compound interest)

On substituting into the formula we have;

\(A = 5000(1+0.04)^{1(5)} \\A = 5000(1.04)^{5} \\A = 5000*1.2166529\\A = 6,083.26\)

Interest earned = Amount - Principal

Interest earned  = $6,083.26 - $5,000

Interest earned = $1,083.26 ≈ $1,083

Hence, the total interest earned in 5 years is $1,083 to the nearest dollars.

Complete question :

How many dimes might he have?

How many coins would he have altogether?

Answer:

11, 12, 13, 14 ;

16, 17, 18, 19

Step-by-step explanation:

Let :

Nickel = n

Dimes = d

Total number of nickels = 5

He has more than 2 times as many dimes as nickels ;

d > 2n

d > 2*5 ; d > 10

He has fewer than 3 times as many dimes as nickels;

d < 3n

d < 3*5 ; d < 15

Meaning he has more than 10 dimes but less than 15.

10 < d < 15

So, d could be ;

11, 12, 13, 14

Number of coins altogether :

11 + 5 = 16

12 + 5 = 17

13 + 5 = 18

14 + 5 = 19