let the number be x and y
x + y = 30 -----(1)
x = y + 15 -----(2)
y + y + 15 = 30
2y = 15
y = 7.5
x = 7.5 + 15 = 22.5
x= 22.5 , y = 7.5
suppose the mean and standard deviation are 74.04 and 9.75, respectively. if we assume that the distribution of ages is mound-shaped and symmetric, what percentage of the respondents will be between 64.29 and 93.54 years old?
Approximately 81.5% of the respondent will be between 64.29 and 93.54 years old.
Given that:
Mean u = 74.04
Standard deviation S.D. = 9.75
Distribution of ages is mound-shaped and symmetric.
We have to find percentage of the respondent between 64.29 and 93.54 years old.
For 93.54
z-score = [tex]\frac{x-u}{S.D}[/tex]
Z score = (93.54 – 74.04)/9.75 = 19.5/9.75 = 2
For 64.29
Z score = (64.29 – 74.04)/9.75 = -9.75/9.75 = -1
Now p-value from z-table:
P(x<93.54) = p(z<2) = 0.97725
P(x>64.29) = p(z>-1) = 0.15866
Probability between 64.29 and 93.54 year old = .97725 – 0.15865
= 0.8186
Percentage of the respondent = 0.8186 * 100 = 81.8%
Therefore, approximately 81.5% of the respondent will be between 64.29 and 93.54 years old.
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Which equation is set up correctly using the Pythagorean Theorem for the triangle below?
9 cm and 14 cm x
A.9² +15²=x²
B.9+z=15
C.15+9=x
D.9²2 +2²=15²
Answer:
A.9^2+15^2=x^2
Step-by-step explanation:
Pythagorean Theorem
a^2+b^2=c^2
Let p and q represent the following statements.
p: Brad Pitt is governor.
9 There are not 51 states in the U. S.
Express the following statement symbolically.
There are 51 states in the U. S.
The statement written symbolically is
AS per the concept of reasoning, the statement written symbolically is ~Q
The term reasoning in math is defined as a drawing logical conclusions based on evidence or stated assumptions
While we looking into the statement P and Q, then we can get it as
p: Brad Pitt is governor.
q: There are not 51 states in the U. S.
Here we have to know that the we have to write the following in the symbolic form, that is written as,
=> There are 51 states in the U. S.
While we looking into the statement, we have identified that the statement is write as the inverse form of the previously given one.
So, the symbolic form is ~Q.
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A culture of bacteria has an initial population of 8600 bacteria and doubles every 5
hours. Using the formula P = Po 24, where P, is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 7 hours, to the nearest whole number?
Answer: The formula for population growth of bacteria with a constant doubling time is P = Po*2^(t/d), where P is the population after t hours, Po is the initial population, t is the time in hours, and d is the doubling time.
Given the initial population of 8600 bacteria and a doubling time of 5 hours, we can substitute these values into the formula:
P = 8600 * 2^(7/5)
To find the population after 7 hours, to the nearest whole number, we can use a calculator to calculate 2^(7/5) which is approximately 3.7 and then multiply it with the initial population.
P = 8600*3.7
P = 31420
So, the population of bacteria in the culture after 7 hours will be around 31420.
Step-by-step explanation:
Pyrotechnicians can use polynomials to plan complex fireworks displays. A firework is launched from a platform 6 feet above the ground at a speed of 200 feet per second. The firework has a 5-second fuse. The height of the firework in feet is given by the polynomial -16t² + 200t + 6, where t is the time in seconds. How high will the firework be when it explodes?
the fireworks will be 612 feet high when it explodes.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, Pyrotechnicians can use polynomials to plan complex fireworks displays. A firework is launched from a platform 6 feet above the ground at a speed of 200 feet per second.
Expression that represents the height of firework = -16t² + 200t + 6
Since The firework has a 5-second fuse.
Thus, the firework will explode at t = 5
So, height at t= 5:
height of firework = -16 * 5² + 200*5 +6
height of firework = -16 * 25 + 1000 +6
height of firework = - 400 + 1000 + 6
Height of firework = 606
Since it started at 6 feet height
Thus total height at firework starts = 606 +6
total height at firework starts = 612
Therefore, the firework will explode at 612 feet in height.
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The ratio of side lengths of a quadrilateral is 3 : 5 : 6 : 9, and its perimeter is 9.6cm. What is the length of the longest side?
The length of the longest side is solved to be 3.76 cm
How to determine the length of the longest sideAn ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
The perimeter o the quadrilateral have a formula that add all the sides together, assuming the factor of the original length is x, the perimeter is solved by
9.6 = 3x + 5x + 6x + 9x
9.6 = 23x
x = 9.6 / 23
x = 0.4174
The length of the longest side
= 9x
= 9 * 0.4174
= 3.76 cm
3.76 cm is the length of the longest side
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What fraction names the equal parts of the whole pizza? Enter your answer in the boxes. Circle is divided into 4 equal parts. Line
If the pizza is divided in to four equal parts , then each equal part is named as "one fourth" .
The fraction is defined as a numerical value that is part of a whole. Fraction is evaluated by dividing a whole into number of parts.
For Example : 1/2 represents the half part of the whole .
The pizza is divided into four equal part ;
So , the total number of parts in the pizza is = 4 parts ,
one part of the pizza will be written in fraction form as : 1/4 ;
We can say that each pizza slice is 1/4 of whole pizza and 1/4 is read out as "one fourth".
The given question is incomplete , the complete question is
What fraction names the 4 equal parts of the whole pizza ?
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Use the screen shot- that has the question on it :)
Answer:
C
Step-by-step explanation:
This looks like a case of multiplying the number of X's by the respective number below it.
For example: the 1/2 has 3 X's, so we multiple (1/2)(3), making it (3/2) or 1.5
Next is the 1 having 2 X's, so (2)(1) is 2
Continuing that trend we get the following
1.5, 4, 2.5, and 3.
So all of our totals are 1.5, 2, 1.5, 4, 2.5, and 3.
Our last step will be adding all these answers together.
1.5 + 2 = 3.5
+ 1.5 = 6
+ 4 = 10
+ 2.5 = 12.5
and finally +3 = a grand total of 15.5 or 15 1/2
k divided by 0.1 = 36 what is k
[tex]\dfrac{k}{0.1} =36[/tex]
Multiply both sides by 0.1:
[tex](\dfrac{k}{0.1} )\times0.1=(36)\times0.1[/tex]
[tex]\fbox{k = 3.6}[/tex]
A fast ferry takes 4 hours to cross a lake an average speed of
108 km/h. On a particular day, it traveled at an average speed
of 94 km/h for 4 hours. What was the remaining distance?
____km
Answer:
The remaining distance will be "56 km".
Step-by-step explanation:
Speed and Time:
The speed (s) of an object seems to be the rate at which it travels from one location to some other. It's also calculated by dividing the distance (d) traveled by the timeframe (t) or duration.
According to the question,
Average speed when cross a late, 108 km/h
On particular day, average speed 94 km/h
Time taken, 4 hours
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^^^^^^
not my work
where I found the answer
The most Ellsworth can afford to pay per year in mortgage payments is
$14,000, and his credit score is currently 498. According to the following table
for a $150,000 mortgage, by how many points would he need to improve his
credit score in order to take a mortgage for $150,000?
FICO
Interest
Score
Rate
720-850
700-719
675-699
620-674
560-619
500-559
5.59%
5.71%
6.25%
7.40%
8.53%
9.29%
A. 2 points
OB. 177 points
O C. 122 points
OD. 62 points
Monthly
Payment
$860
$872
$924
$1039
$1157
$1238
62 points, he would need to improve his credit score in order to take a mortgage for $150,000.
What is a mortgage?
It is an agreement between you and a lender that allows you to borrow money to purchase or refinance a home and gives the lender the right to take your property if you fail to repay the money you've borrowed. A mortgage is a type of loan that's used to finance the property. A mortgage is a type of loan, but not all loans are mortgages. Mortgages are “secured” loans.
To calculate the monthly payment, we can use the formula:
M = P [i(1 + i)^n] / [(1 + i)^n – 1]
Where M is the monthly payment, P is the loan amount, i is the interest rate, and n is the number of payments (in this case, the number of months in 30 years)
Plugging in the values,
M = 150000 * (0.0929 / 12) / [ (1 + (0.0929 / 12))^(12 * 30) - 1]
This gives a monthly payment of $1238.
To find out how many points he needs to improve his credit score, we can compare this monthly payment to the maximum monthly payment he can afford, which is $14,000.
If $1238 is more than $14,000, he would need to improve his credit score to a point where the monthly payment would be less than $14,000. By looking at the table, we can see that the interest rate for credit score of 620-674 is 7.40%.
Hence, (D) option is the correct answer.
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One angle of an isosceles triangle measures 120°. What measures are possible for the other two angles? Choose all that apply.
10°
30°
80°
50°
Answer:
b) 30°
Additional information:-
One angle (x) = 30° Both angles (2x) = 60°Step-by-step explanation:
We know that,
→ The other two angles of the isosceles triangles are equal.
Formula we use,
→ <A + <B + <C = 180°
Forming the equation,
→ 120° + x + x = 180°
Now the value of x will be,
→ 120° + x + x = 180°
→ 120° + 2x = 180°
→ 2x = 180° - 120°
→ 2x = 60°
→ x = 60°/2
→ [ x = 30° ]
Hence, option (b) is correct.
Greg calculated that he has to drive at least 50 miles per hour on the highway to get to his destination on time. What number line shows the solution set to this inequality
The number line which best conveys Gregg's situation is B.
line B is the answer and the image is attached,
Since Greg has calculated that his least or minimum speed should be 50 miles per hour ,
Then the line starts at 50 with the starting point shaded due to the at least notation.
Then at least means that,
Gregg may need to travel at a higher speed than 50, so the direction of the arrow moves to the right of the number line depicting a possible increase in Gregg's speed.
Therefore, the number line which best conveys Gregg's situation is B.
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What percent of the men surveyed shop online? Round your answer to the nearest whole number percent.
A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $25. The total cost to rent 5 chairs and 6 tables is $65. What is the cost to rent each chair and each table?
The cost to rent each chair and table, based on the total cost to the party rental company, is:
Cost to rent chair = $ 2.50Cost to rent table = $ 8.75How to find the cost to rent the chairs and tables ?Let x be the cost of renting one chair and y be the cost of renting one table.
From the first piece of information given, we can write the equation:
3x + 2y = 25
From the second piece of information given, we can write the equation:
5x + 6y = 65
Solving these equations using elimination gives:
3x + 2y = 25
5x + 6y = 65
15x + 10y = 125
15x + 18y = 195
Subtracting gives:
0x + 8y = 70
y = $ 8.75
The cost to rent a chair is:
3x + 2 (8.75) = 25
3x + 17.5 = 25
3x = 7.5
x = $ 2.5
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For parties of six or more, a restaurant adds a 20% gratuity (or tip). If a
dinner bill for a large party comes to $148.25, find the total dinner bill with
tip. $177.90
The total dinner bill was $177.90 including a tip of 20%.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
Given that, a restaurant adds a 20% gratuity (or tip), a dinner bill for a large party comes to $148.25, we need to find the total dinner bill with tip.
The total bill will be = 148.25 + 20% of 148.25
= 148.25 + 20/100 × 148.25
= 148.25 + 0.2 × 148.25
= 148.25 + 29.65
= 177.90
Hence, the total dinner bill was $177.90 including a tip of 20%.
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one eighth of al's coins are quarters and the rest are nickels. if the total value of the coins is $3.60, how many of each type of coin does he have?
Number of quarters is 6 and number of nickels are 42.
One eighth of Al's coins are quarters, so if we let x be the total number of coins, then x/8 is the number of quarters Al has.
We know that:
Quarters are worth $0.25 and nickels are worth $0.05 and total value of the coins is $3.60
so, x/8 * $0.25 + (x-x/8) * $0.05 = $3.60
=> x/8 * 0.25 + 7x/8 * 0.05 = 3.60
multiplying both sides by 8 to cancel out 8, we get
=> x*0.25 + 7x * 0.05 = 28.8
=> x/4 + 7x/20 = 28.8
=> (5x + 7x)/20 = 28.8
=> 12x = 576
=> x= 48
x/8 = 6 and (x-x/8) = 42
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The length of the room are y2 – 5y = 750 , y(y – 5) + 750 = 0 and (y + 25)(y – 30) = 0
How to determine the expressionit is important to note that the formula for calculating the area of a rectangle is expressed as;
A = lw
Such that;
A is the area of the rectanglel is the length of the rectanglew is the width of the rectangleFrom the information given, we have that;
Length = y
Width = y - 5
Area = 750 square feet
Substitute the values into the formula
750 =y(y - 5)
expand the bracket
750 = y² - 5y
y² - 5y- 750 = 0
This is factorized to give;
(y + 250 (y - 30)
Hence, the expression is y² - 5y- 750 = 0
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Please help I need the answers ASAP!
Part A:
Find m∠2,
Since ∠1 and ∠2 are alternate interior angles, they are equal. So, m∠2=60°
Part B:
Find m∠3,
Since ∠2 and∠3 are supplementary, the sum of their measures is 180°. So, m∠3=180°-60° which is 120°.
Simply the expression & explain
Answer:
780
Step-by-step explanation: The answer is 780!
how many times does 6 go into 3594?
Answer: 599 times
Step-by-step explanation: 3594/6=599
Use the distributive property to write three different expressions that are equivalent to. 24xy + 48xz
number of ice cream bars needed to sell 100 each weekend for a year
I year of weekends= 105days therefore 105, therefore you need 105 ice cream bars? hoped this helped
An angle is two collinear rays with a common endpoint. Find an example that contradicts this definition. How would you change the definition to make it more accurate? (5 points)
Part B: Give an example of an undefined term and how it pertains to angles
As per the collinear point, the common endpoint is called the vertex of the angle, and the rays are called the sides of the angle.
The term collinear point in math is defined as a set of three or more points that exist on the same straight line
Here we have given that an angle is two collinear rays with a common endpoint.
And we need to find an example that contradicts this definition.
Here we also know that an angle is the union of two noncollinear rays with a common endpoint.
Then the common endpoint is called the vertex of the angle and the rays are called the sides of the angle.
And it is measure of an angle is a number representing the spread of the two arms of the angle.
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are 1/2x + 3/4 - 5/8x - 7/8 and 1/8(x + 1) equivalent expressions? show your work help plss
Answer: No they are not.
Step-by-step explanation:
1/2x and -5/8x are like terms, if subtracted you get 1 1/8x. But then you are left with an unlike term, 3/4 so your first equation would equal out to 1 1/8x + 3/4
Now for equation 2, you use your distributive property and get 1/8(x)=1/8x
Then you must distribute 1/8(1)=1/8
1/8x + 1/8
So, 1 1/8x + 3/4 ≠ 1/8x + 1/8
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Sidney made root beer floats for her friends when they came over. The table shows the ratio of cups of ice cream to cups of soda used to make the floats.
Ice Cream (cups) Soda (cups)
3.5 10.5
8 24
12.5 37.5
15 ?
At this rate, how much soda will Sidney use for 15 cups of ice cream?
30 cups
35 cups
40 cups
45 cups
The number of cups of soda Sidney will use for 15 cups of ice cream is 45 cups of soda.
What is a ratio?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,
From the table,
3.5 cups of ice cream = 10.5 cups of soda.
This means,
1 cup of ice cream = 3 cups of soda.
Multiply 15 on both sides.
15 cups of ice cream = 45 cups of soda.
Thus,
45 cups of soda are used.
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8(r+1) Distributive property
Answer:(8 x r)+(8 x 1)
Step-by-step explanation:
[tex]8(r+1)[/tex]
Distribute:
[tex](8)(r)+(8)(1)[/tex]
[tex]\fbox{8r + 8}[/tex]
I just need the answer to W
The value of w in the rhombus is 19 degrees
How to determine the value of w?
From the question, we have the following parameters that can be used in our computation:
Angle CFD = 2w
Angle FED = 52 degrees
The figure is a rhombus
using the above as a guide, we have the following:
2w + 52 = 90
This is so because the angles in the base of the individual triangle are equal
Evaluate the like terms
2w = 38
Divide by 2
w = 19
hence, the solution is w = 19
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Can someone please help me with this? I need help ASAP
Answer:
58
Step-by-step explanation:
error: 64+2p = 180. he missed 1 p.
so 2p =180-64
p = 58
An artist draws a stained glass window to scale. The actual window will have a length of 5ft and a width of 2ft. The scale from the drawing to the window is 2in to 1 ft. What is the width of the drawing?
Answer: 4 in
Step-by-step explanation: