in a normal distribution with a mean of 90 and a standard deviation of 5, which of the following scores lie within one standard deviation of the mean? select one: a. 5-90 b. 80-100. c. 85-95. d. 90-95.

Both slope are equal so we can say that both lines are parallel

slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").

Line a: 2x + y = 10

Line b:

- 6x – 3y = 3

and line

Line a: 2x + y = 10

= slope of line A is

2x + y = 10

y = -2x+10

slope = -2

- 6x – 3y = 3

-3y = 6x +3

x = -2y -1

slope  = -2

in  this case both slope are equal so we can say that both lines are parallel

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The piecewise function's domain and range are all real numbers, excluding x = 6, and all real numbers, respectively.

The broad range of values within which we are permitted to enter into our function is known as the area of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.

The piecewise function is a function.

In the image that is attached, a function is shown.

The function's defined values are its domain, and its attainable values are its range.

With the exception of the x = 6 range, all real numbers fall inside the domain.

As a result, choice c is the right one.

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The approximate solutions to the equation is (0.655, -2.618)

From the question, we have the following parameters that can be used in our computation:

-2x

|-3 + 1| =

-2√x - 1

Express the equation properly

So, we have the following representation

-2x|-3 + 1| = -2√x - 1

This gives

-4x = -2√x - 1

Next, we split the equation

y = -4x

y = -2√x - 1

To solve graphically, we plot the equation and write out the point of intersection

Hence, the solution is (0.655, -2.618)

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Answer:

[tex]\frac{- 7}{b - y}[/tex]

Step-by-step explanation:

Algebraic manipulation (i.e. a process involving rearranging or rewriting variables and, multiplication or division, to achieve an algebraic expression in a desired form) will be applied:

The expression in the denominator (y - b) will be algebraically manipulated by being multiplied by negative one:

[tex](y - b)[/tex]×[tex](-1)[/tex]

The parenthesis will be expanded by applying the Distributive Law. The derived variables will be rearranged to achieve the desired form of the algebraic expression:

[tex][(-1)(y)] - [(-1)(b)][/tex] = [tex]-y - (-b)[/tex]

                               = [tex]-y + b[/tex]

                               = [tex]b - y[/tex] (Desired form achieved)

∴The multiple factor of negative one will also need to be multiplied with the numerator of the fraction for balance. This is because the negative one (that is being multiplied with the denominator) was NOT present originally:

[tex](-1)[/tex]×[tex](7)[/tex] = [tex]-7[/tex]

∴The desired form of the fraction is:

     [tex]\frac{-7}{b - y}[/tex]

The fraction 7/(y - b) after changing the denominator (b - y) becomes - 7/(b - y).

Fraction is a comparison between two mathematical quantities or numbers in general.

The number which is being compared is called Numerator and the with whom it is compared is called Denominator.

In mathematical words, if a fraction is look like A/B where A and B are two numbers then A is called Numerator and B is called Denominator.  

Here given the fraction is, 7/(y - b)

So here numerator = 7 and denominator = y - b

We have to change the denominator that is (y - b) with (b - y).

Rearranging the fraction we get,

7/(y - b) = 7/[- (b - y)] = - 7/(b - y).

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a) The probability that he will make both free throws is 81 %

b) The probability that he will make at least one free throw is 18 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the particular NBA player makes 90 % of his free throws

Now , the equation will be

The probability that the first shot going in = 90 %

And , the probability that the first shot does not go in = 10 %

So , there are 4 scenarios when he is awarded 2 free throws

Both the shots going in = 90 % x 90 %

Both the shots not going in = 10 % x 1- %

Missing one shot and and one shot going in = 10 % x 90 %

And , One shot going in and missing one shot = 90 % x 10 %

a)

Now , the probability that he will make both free throws = Both the shots going in

Substituting the values in the equation , we get

The probability that he will make both free throws = 0.9 x 0.9 = 0.81

The probability that he will make both free throws = 81 %

b)

The probability that he will make at least one free throw = Missing one shot and and one shot going in = 10 % x 90 %   +   One shot going in and missing one shot = 90 % x 10 %

Substituting the values in the equation , we get

The probability that he will make at least one free throw = 0.1 x 0.9 + 0.9 x 0.1

The probability that he will make at least one free throw = 0.09 + 0.09

The probability that he will make at least one free throw = 0.18

The probability that he will make at least one free throw = 18 %

Hence , the probabilities are solved

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The equation in standard form representing the scenario where Briana has $3 in her piggy bank and has all quarters and dimes, using x for the number of quarters and y for the number of dimes, is [tex]25x + 10y = 300[/tex].

Let x be the number of quarters and y be the number of dimes Briana has in her piggy bank.

The value of each quarter is 25 cents or 0.25 dollars, and the value of each dime is 10 cents or 0.10 dollars. Therefore, the total value of the coins in Briana's piggy bank can be expressed as:

[tex]0.25x + 0.10y[/tex]

Since Briana has $3 in her piggy bank, we can set up the following equation:

[tex]0.25x + 0.10y = 3.00[/tex]

To write this equation in standard form ([tex]Ax + By = C[/tex]), we need to clear the decimals by multiplying both sides of the equation by 100:

[tex]25x + 10y = 300[/tex]

Therefore, the equation in standard form that represents this scenario is:

[tex]25x + 10y = 300[/tex]

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Step-by-step explanation:

the area of a circle is

pi×r²

r being the radius (1.68 m).

the area of half a circle is therefore

pi×r²/2

in our case

pi× 1.68²/2 = pi× 2.8224/2 = pi×1.4112 =

= 4.433415553... m² ≈ 4.43 m²

The area of the shaded semicircle is  1.11 meters squared.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed shape, two-dimensional .

The area of shape is the space enclosed within the perimeter or the boundary of a given shape.

The area of a circle is expressed as ;

A = π[tex]r^{2}[/tex]

where r is the radius of the circle.

Therefore the area of a semi circle will be :

A = 1/2  π[tex]r^{2}[/tex]

r = d/2

r = 1.68/2 =0.84

A = 1/2 × 3.14 × 0.84 ×0.84

 = 1.11 meter squared.

Therefore the area of the shaded semi circle is 1.11 meters squared.

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As per the discount, the customer will only need to pay P4,950 on May 12.

Discounts are a common practice in business transactions, where the seller offers a reduction in the price of goods or services as an incentive for the buyer to make a purchase.

The terms of the sale are as follows: 2/10, 1/15, n/30. This means that the customer is entitled to a 2% discount if they pay within 10 days, or a 1% discount if they pay within 15 days. Otherwise, the full amount is due within 30 days.

The customer makes a partial payment of P1,000, which means that they still owe P5,000. However, since the discount is only given upon full payment, the customer is not eligible for any discounts at this point.

Assuming that the customer pays the balance on May 12, they will have taken 11 days to make the payment. Since this is within the 15-day discount period, they are entitled to a 1% discount.

The calculation of the discount is as follows: P5,000 x 1% = P50. Therefore, the customer will only need to pay is calculated as,

=> P5,000 - P50 = P4,950

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Complete Question:

On May 1, RVQ Company sold goods for P6,000 on terms of 2/10, 1/15, n/30. Customer made a partial payment of P1,000 discounts are given only upon full payment of an account. The customer pays the balance on May 12, RVQ will receive on May 12 the amount of

Answer:

Step-by-step explanation:

Find common denominator.

1/x + x-1/9x = 1  => 9/9x + x-1/9x = 1  (The common denominator is 9x.)

Combine like terms.

9 + x - 1 / 9x = 1  =>  x + 8/ 9x = 1

Cancel out 9x from denominator. What you do to one side, you do to the other.

(9x)(x + 8/9x) = 1(9x)  =>  x + 8 = 9x

Solve for x.

8 = 8x  =>  x = 1  (subtract x from both sides at the beginning and then simplify.)

Answer:

B

Step-by-step explanation:

the zeros are the values of x on the x- axis where the graph crosses.

the graph crosses the x- axis at x = 3 and x = 6

then

the zeros are x = 3 and x = 6

The order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].

Using the given information, we can find the common ratio of the geometric sequence A.

First, we can use the equation T₂² = T₁ T4 to find T4. Substituting n = 4, we get:

T₂² = T₁ T4

20² = T₁ T4

T4 = 400/T₁

Next, we can use the equation T5 = 20 to find T₁r⁴:

T5 = T₁r⁴

20 = T₁r⁴

We can now substitute T4 in terms of T₁ in the equation above:

20 = T₁r⁴

20 = T₁(400/T₁)r⁴

20 = 400r⁴

r⁴ = 1/20

Therefore, the common ratio r = (1/20)^(1/4) = 0.5.

To find the order of the first term whose value is greater than 106, we can use the formula for the nth term of a geometric sequence:

Tn = T₁r^(n-1)

We want to find the smallest value of n such that Tn > 106. Substituting r = 0.5 and rearranging, we get:

T₁(0.5)^(n-1) > 106

T₁ > 212(0.5)^(1-n)

Since T₁ > 0, we can take the logarithm base 0.5 of both sides:

log(0.5)(T₁) < log(0.5)(212) + (n-1)

Solving for n, we get:

n > 1 + [log(0.5)(T₁) - log(0.5)(212)]

Therefore, the order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].

Note that the exact value of this order depends on the value of T₁, which was not given in the original problem statement.

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For removing all the perfect squares of √(39y^9), we need to factor out any perfect squares from the expression under the square root.

To get rid of all the perfect squares in (39y9), factor out any perfect squares in the expression under the square root.

First, by factoring 39 and y9, we can simplify the expression under the square root:

[tex]√(39y^9) = √(313y^8y) = √(313*(y^4)^2*y)[/tex]

Because (y4)2 is a perfect square, we can take it out from under the square root:

[tex]√(39y^9) = √(313(y^4)^2y) = (y^4)√(313*y)[/tex]

By removing all of the perfect squares from (39y9), we get:

[tex](y^4)√(313y)[/tex]

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A plumber worked 3. 5 hours for AED 1,075 in total. He added AED 200 for supplies to the customer's bill hourly rate of the plumber is AED 364.29.

How much is charged, paid, or earned for each hour worked?

Instead of paying for the things the advisers try to sell you, you pay a set or hourly charge for their time.

We must first deduct the price of the materials from the plumber's overall profits in order to get his hourly rate:

Income equals AED 1,075 plus AED 200, or AED 1,275.

After that, we may split his total income by the quantity of hours he put in:

Hourly fee is calculated as follows: AED 1,275 / 3.5 hours of work.

Hourly rate is 364.29 AED.

The plumber's hourly charge is therefore AED 364.29.

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Answer:ab

Step-by-step explanation:

because..........

The value of x and y in the geometric sequence are 1/r and 1

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

If the first term of the sequence is a ,second term is ar , third term = ar²

r = ar²/ar

In the sequence 2y, 2xy, 2, xy/2, ...

r = 2y/2xy

therefore r = 1/x

r = 2/2xy

r = 1/xy

therefore 1/x = 1/xy

therefore y = 1

x = 1/r

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The inverse of a function f(x)=2x + 1 include the following: A. H(x) = 1/2x - 1/2

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;

f(x) = y = 2x + 1

x = 2y + 1

By rearranging the equation, we have the following:

2y = x - 1

y = (x - 1)/2

H(x) = 1/2(x) - 1/2.

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The value of b is given as follows:

b = 12.5 m.

The value of b is obtained applying the proportions in the context of the problem.

The rule of three is given as follows:

5 m - b m.

4 m - 10 m.

Applying cross multiplication, the value of b is obtained as follows:

4b = 50

b = 50/4

b = 12.5 m.

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The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is 2/5

A cylinder is a three-dimensional shape that consists of two parallel circular bases connected by a curved lateral surface. The volume of a cylinder is the amount of space contained within the cylinder. It can be calculated using the formula:

Volume of cylinder = πr^2h

Let's denote the height and radius of Cleopatra's water clock as h_c and r_c, respectively, and the height and radius of Ptolemy's water clock as h_p and r_p, respectively. Since both clocks drain uniformly, we can use the formula for the volume of a cylinder to relate the height and radius of each clock to the time it takes to drain:

Volume of Cleopatra's clock =[tex]\mathrm{ \pi r_c^2h_c}[/tex]

Volume of Ptolemy's clock = [tex]\mathrm{\pi r_p^2h_p}[/tex]

Since Cleopatra's clock drains in 4 hours, the rate of draining is (Volume of Cleopatra's clock) / (4 hours), and similarly for Ptolemy's clock. We are given that after 2 hours of draining, both clocks have the same water height. Therefore, we can set the two rates of draining equal to each other and solve for the ratio of heights:

(Volume of Cleopatra's clock) / (4 hours) = (Volume of Ptolemy's clock) / (5 hours)

[tex]\pi r_c^2h_c / 4 = \pi r_p^2h_p / 5[/tex]

[tex]h_c / h_p = (r_p / r_c)^2 \times (5 / 4)[/tex]

We are not given the values of the radii, but we can see that the ratio of heights depends only on the ratio of the radii squared. Therefore, we don't need to know the actual sizes of the clocks, only the ratio of their radii. Let's call this ratio x:

[tex]x^2 = (h_c / h_p) \times(4 / 5)[/tex]

After two hours of draining, the water height in both clocks is the same, so we can set the volume of water in each clock equal to each other:

[tex]\pi r_c^2(h_c - 2h_c/4) = \pi r_p^2(h_p - 2h_p/5)[/tex]

[tex]\pi r_c^2h_c/2 =\pi r_p^2h_p/5*3[/tex]

[tex]r_c^2h_c/2 = r_p^2h_p/15[/tex]

Now, we can solve for the ratio of water heights after each clock has been draining for three hours:

Water height in Cleopatra's clock after 3 hours = [tex]\mathrm{h_c - (3/4)h_c = (1/4)h_c}[/tex]

Water height in Ptolemy's clock after 3 hours = [tex]\mathrm{ h_p - (3/5)h_p = (2/5)h_p}[/tex]

([tex]h_p[/tex]  / (2/5)[tex]h_p[/tex] ) = ((1/4)[tex]h_c / h_c[/tex])

([tex]h_p[/tex]  / (2/5)) = 1/4

[tex]h_p[/tex] = 2/5 * 1/4

[tex]h_p[/tex] = 1/10

Therefore, the fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is:

[tex]h_p / h_c[/tex]= 1/10 / (1/4) = 2/5

And the fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been draining for three hours is:

[tex]h_c / (2/5)h_p[/tex] = (1/4) / (2/5)(1/10) = (1/4) / (1/20) = 5/4

Hence,

The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is: 2/5

The fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been drained for three hours is: 5/4.

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Answer: 25% of 50 is 25/2 or 12½ as a fraction and 12.5 as a decimal.

Let's find 25% of 50.

Explanation:

25% of 50 can be written as 25% × 50

= 25/100 × 50

= 25/2 = 12½ = 12.5

Thus, 25% of 50 is 25/2 or 12½ as a fraction and 12.5 as a decimal.

Answer:

(4,3)

Step-by-step explanation:

We can make advantage of the distributive property of multiplication over addition, which says that a(b + c) = ab + ac. As a result, -55 is the simplified expression.

When you multiply a value by a sum, the distributive property of multiplication over addition is put to use. For instance, you wish to multiply 5 by the product of 10 plus 3. Since the numbers are similar terms, we typically add the numbers first and then multiply by 5=> 5(10 + 3) = 65.

An algebraic principle known as the distributive property indicates that it is necessary to multiply each of the two integers by the factor being multiplied by the sum or difference of two terms.

Using this property, we can expand the expression as follows:

(2 − 3)(7 2 − + 8) = 2(7 2 − + 8) − 3(7 2 − + 8)

Now we can simplify each term separately:

2(7 2 − + 8) = 2(49 − 2 + 8) = 2(55) = 110

and

−3(7 2 − + 8) = −3(49 − 2 + 8) = −3(55) = −165

Therefore, putting the results together, we have:

(2 − 3)(7 2 − + 8) = 110 − 165 = -55

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Answer:

1/4

Step-by-step explanation:

On a graph that's up 1 over 4 and its rise over run or (rise/run)

The probability that no two of them celebrate their birthday in the same month is very low.

There are 12 months in a year, so the probability that the first person has a birthday in a particular month is 1/12. The probability that the second person does not have a birthday in the same month is 11/12, since there are 11 months left that the second person's birthday can fall in. The probability that the third person does not have a birthday in any of the two previously chosen months is 10/12, and so on.

Therefore, the probability that none of the 12 people have a birthday in the same month is:

P = (1/12) x (11/12) x (10/12) x ... x (2/12) x (1/12)

which is approximately 0.00010578, or about 0.01%.

So the probability that no two of them celebrate their birthday in the same month is very low.

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The ratio of cups of flour to water for 6 batches is 18:6

18:6 = 3:1

The ratio is maintained.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Two batches:

The ratio of cups of flour to water.

= 6: 2

= 3:1

Now,

For 1 batch.

The ratio of cups of flour to water.

= 3 : 1

Now,

For m batches.

The ratio of cups of flour to water.

= 3m : 1m

So,

For m = 6

The ratio of cups of flour to water.

= 18 : 6

Thus,

The ratio of cups of flour to water for 6 batches is 18:6.

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The complete question.

For two batches the ratio is 6 cups of flour to 2 cups of water,

This means for every 3 cups of flour, you need 1 cup of water.

The ratio 3:1 is maintained.

Find the ratio for 6 batches

The required shortest distance between the building and the end of the ramp, if the doorway is 1.3 feet above the parking lot, is 1.3 feet.

The slope is defined as the ratio measure of rise to measure of the run.

Here,
The shortest possible distance between the building and the end of the ramp, if the doorway is 1.3 feet above the parking lot, is 1.3 feet.

This is because, if the doorway is 1.3 feet above the parking lot, the ramp will need to rise 1.3 feet in order for a person or vehicle to be able to enter the building. The length of the ramp will be equal to the rise, so in this case, the shortest possible distance between the building and the end of the ramp would be 1.3 feet.

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The measure of each interior angle of a regular polygon having 15 sides is equal to option B: 156°.

A polygon is an enclosed figure composed of more than three straight lines. To find the measure of each interior angle of a regular polygon having n sides, we would first find the total sum of interior angles of this polygon. The formula is:

(n-2) × 180°

= (15-2) × 180°

= 13 × 180°

= 2340°

We, here, found that the sum of all interior angles of a regular polygon having 15 sides is equivalent to 2340°. Now, to find the measure of each angle, we can divide this sum by the number of sides as:

2340/15 = 156°.

Therefore, the measure of each angle of a regular polygon having 15 sides is equivalent to 156°.

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Complete question is:

Find the measures of each interior angles of a regular polygon having 15 sides.

A. 106°

B. 156°

C. 206°

D. 256°

It will take Daniel approximately 2 hours and 52 minutes (172.066 minutes) to complete the triathlon.

To estimate how long it will take Daniel to complete the triathlon, we can calculate the time it will take him to complete each leg of the race and add them together.

Swim:

Distance = 0.93 miles

Speed = 2.2 mph

Time = Distance / Speed = 0.93 miles / 2.2 mph = 0.4236 hours = 25.416 minutes

Bike:

Distance = 24.8 miles

Speed = 17.8 mph

Time = Distance / Speed = 24.8 miles / 17.8 mph = 1.3933 hours = 83.6 minutes

Run:

Distance = 6.2 miles

Speed = 5.9 mph

Time = Distance / Speed = 6.2 miles / 5.9 mph = 1.0508 hours = 63.05 minutes

Total time = Swim time + Bike time + Run time

Total time = 25.416 minutes + 83.6 minutes + 63.05 minutes

Total time = 172.066 minutes

Therefore, it took  172.066 minutes which is approximately equal to 2 hours and 52 minutes by Daniel to complete the triathlon.

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The value of the expression when evaluated is -15

From the question, we have the following parameters that can be used in our computation:

The table of values for the function f(x)

The expression to evaluate is given as

f-1(3) - 4 * f(6)

Using the above as a guide, we have the following:

f-1(3) = 5

f(6) = 5

substitute the known values in the above equation, so, we have the following representation

f-1(3) - 4 * f(6) = 5 - 4 * 5

Evaluate

f-1(3) - 4 * f(6) = -15

Hence, the solution is -15

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The equation that represents this situation is $6t - $450 ≥ $1000.

The number of tickets that should be sold is 242.

The form of the equation is:

total revenue - total cost ≥ $1000

(cost of one ticket x number of tickets sold) -  cost of pizza and drinks ≥ $1000

($6 x t) - ($200 + $250) ≥ $1000

$6t - $450 ≥ $1000

$6t ≥ $1000 + $450

$6t ≥ $1450

t ≥ $1450 / 6t

t ≥ 242

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(a) The angle measurement of first unknown angle is c = 80 degrees

(b) The angle measurement of second unknown angle is y = 110 degrees

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees

The angle measurement of first unknown angle will be:

a + b + c = 180  (sum of angles in a triangle is 180 degrees)

c = 180 - a - b

c = 180 - 30 - 70

c = 80 degrees

(b) The angle measurement of second unknown angle will be:

y = 180 - b  (sum of angles on a straight line is 180 degrees)

y = 180 - 70

y = 110 degrees

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