The daughter's age is 7 years old.
What is the equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a parent is 20 years older than twice his daughter's age, and he was half of his present age 17 years back.
Let the age of the parent be x,
He/she was half of the age 17 years back, then,
x/2 = x-17
x = 34
Therefore, parent's present age is 34 years.
He is 20 years older than twice his daughter's age,
Let his daughter's age be y,
2y+20 = 34
2y = 14
y = 7
Hence, his daughter's age is 7 years old.
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The sum of two numbers is 5
Wouldn't the answer be 1 and 4?
As a private contractor for a septic tank cleanup company, you oversee the draining of septic tanks in the county. Your company uses a truck with a storage tank capable of holding 30,500 gallons of waste.
Is there enough storage in the truck to drain a full septic tank in the shape of a cube measuring 191 inches on each side? (231 cubic inches in 1 gallon.)
There is enough storage in the truck. The volume of the septic tank is about 25,219 gallons.
There is enough storage in the truck. The volume of the septic tank is about 30,164 gallons.
There is not enough storage in the truck. The volume of the septic tank is about 36,481 gallons.
There is not enough storage in the truck. The volume of the septic tank is about 6,967,871 gallons.
There is not enough storage in the truck. The volume of the septic tank is about 7,045,500 gallons.
There is enough storage in the truck. The volume of the septic tank is about 30,164 gallons.
How to determine if there is enough storage in the truck to drain a full septic tank?Given that:
Your company uses a truck with a storage tank capable of holding 30,500 gallons of waste.
A full septic tank in the shape of a cube measuring 191 inches on each side.
First, calculate the volume of the septic tank:
Volume of septic tank (V) = S³
where S is the side length of the septic tank
S = 191 inches
V = S³
V = 191³ = 6967871 cubic inches
Since we have 231 cubic inches in 1 gallon:
V = 6967871 / 231 = 30,164 gallons
Thus, the capacity of the full septic tank is 30,164 gallons
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I need help with this
B(x) as a product of linear factors is B(x) = (x+2)(x+7)(x-1)
What is a linear factor?The linear factors of a polynomial are the first-degree equations that are the building blocks of more complex and higher-order polynomials. Linear factors appear in the form of ax + b and cannot be factored further.
if ( x+2) is a factor of the polynomial, then x+2 can divide the polynomial without remainder.
see attached document for detailed division of the polynomial [tex]x^{3}+8x^{2} +5x-14[/tex].
In conclusion B(x) as a product of linear factors is B(x) = (x+2)(x+7)(x-1)\
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Solve for x. √x+3 = 6 A.3 B.9 C.33 D.36
Answer:
C. 33
Step-by-step explanation:
Given:
[tex]\sqrt{x+3}=6[/tex]
Solution:
(square both sides)
[tex]x+3=6^{2}[/tex]
[tex]x+3=36[/tex]
[tex]x=36-3[/tex]
[tex]x=33[/tex]
Answer is 33
option C
emma ray and norman shared 4/5 of a pizza. Do you think thet had 1/3 each? yes or no?
Answer: ya
Step-by-step explanation:bc
Find the difference, and explain how you did it. Explain both the number part and the sign
4-(-6)
Answer:
10
Step-by-step explanation:
The 2 subtracting signs become addition, which is 4 + 6
Your body mass index (BMI) is your weight by kilograms divided by the square of your height in meters. Online BMI calculators allow you to enter weight in pounds and height in inches. High BMI is a common but controversial indicator of being overweight or obese. A study by the National Center for Health Statistics found that the BMI of American young women (ages 20-29) is approximately Normally distributed with mean 26.8 and standard deviation 7.4
Using z-score calculations, we can say that around 13.14%of the young women have a BMI (Body Mass Index) of less than 18.5 and are underweight.
How to find the probability from z-score?The formula for z-score is;
z = (x' - μ)/σ
We are given;
Population Mean; μ = 26.8
Population standard deviation; σ = 7.4
Average BMI; x' = 18.5
Thus;
z = (18.5 - 26.8)/7.4
z = -1.12
From online p-value from z-score calculator, we have;
p-value = 0.1314 = 13.14%
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Complete question is;
Your body mass index (BMI) is your weight by kilograms divided by the square of your height in meters. Online BMI calculators allow you to enter weight in pounds and height in inches. High BMI is a common but controversial indicator of being overweight or obese. A study by the National Center for Health Statistics found that the BMI of American young women (ages 20-29) is approximately Normally distributed with mean 26.8 and standard deviation 7.4
People with BMI less than 18.5 are often classed as “underweight.” What percent of young women are underweight by this criterion?
If log₂(4x + 6) = 4, then x = ____
You may enter the exact value or round to 4 decimal places.
Answer: -1/2
Step-by-step explanation: To solve this problem, we can use the properties of logarithms to isolate the variable x on one side of the equation. The properties of logarithms tell us that the logarithm of a product is the sum of the logarithms of the factors, and that the logarithm of a power is the exponent times the logarithm of the base.
If log₂(4x + 6) = 4, we can rewrite the left side of the equation as follows: log₂(4x + 6) = log₂(2^4 * (2x + 3))
Then, using the property of logarithms that the logarithm of a product is the sum of the logarithms of the factors, we can simplify the equation as follows: log₂(4x + 6) = 4 + log₂(2x + 3)
Now, we can use the property of logarithms that the logarithm of a power is the exponent times the logarithm of the base to simplify the equation even further: log₂(4x + 6) = 4 + 1 * log₂(2x + 3)
Since the logarithm of a power is the exponent times the logarithm of the base, this means that the logarithm of a number is the logarithm of that number divided by the logarithm of the base. Therefore, we can divide both sides of the equation by log₂ to isolate the variable x on one side of the equation:
log₂(4x + 6) / log₂ = 4 + 1 * log₂(2x + 3) / log₂
(4x + 6) / 1 = 4 + (2x + 3) / 1
4x + 6 = 4 + 2x + 3
4x + 6 = 2x + 7
2x = -1
x = -1/2
Therefore, if log₂(4x + 6) = 4, then x = -1/2.
5 1/2 + 3/4 Give your answer in its simplest form.
Answer:
5 1/2 + 3/4
11/2 + 3/4
22+3/4
25/4
=6 1/4
Cost of a sled = $99.50, markup = 95%
Answer:
take wholesale cost and multiply it by 95%, then add to the original value
another way, just multiply by 1.95
Retail cost: 1.95*($99.50) = $194.03
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
So the sales price of the sled is 100% + 95 % = 195 % of the cost
= 1.95 * cost = 1.95 * 99.50 = 194.03 dollars
A collector's model racecar is scaled so that 1 inch on the model equals 6 1/4 feet on the actual car. If the model is 2/3 inch high, how high is the actual car? explain
Answer:
50 inches, or 4 1/6 feet
Step-by-step explanation:
If one inch is equal to 6 1/4 feet, we can translate this number from feet to inches.
4 1/6 feet = 75 inches.
Now we can take 75 and find out 2/3 of it.
2/3 of 75 is 50.
The answer is 50 inches.
If you want to convert the answer from feet to inches, its simple.
12 × 4 = 48
50 - 48 = 2
2 inches is equal to 1/6 of a foot.
The answer in feet, is 4 1/6 foot.
Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other.
D
A
E
C
B
In parallelogram ABCD, show triangle ADC is congruent to triangle CBA
O In parallelogram ABCD, show triangle DEA is congruent to triangle CEB
O In quadrilateral ABCD with AB congruent to CD and AD is congruent to BC, show ABCD is a parallelogram
O In parallelogram ABCD, show DE is congruent to BE and AE is congruent to CE
The conjecture and rephrased statement of proof to demonstrate that the diagonals of a parallelogram cross each other, taking into account the provided figure, is: DE and EB are congruent to one another in the parallelogram EFGH, while AE is congruent to EC.
Define Parallelogram.A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
The parallelogram's diagonals are the lines connecting its two opposed ends. Sharing into two equal portions is known as bisecting. Congruent refers to a copy that has the same dimensions as the original and may therefore be used in place of it. When the diagonals of a parallelogram bisect one another, it signifies that they split into two equal pieces that are congruent with one another.
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Directions: Write an equation of the line in slope intercept form from the given points (-2, 6) & (0, 4)
Answer:
y = -x + 4
Step-by-step explanation:
m = y2-y1 / x2-x1
m = 4-6/ 0-(-2)
m = -2/2
m = -1
y = -x + b
4 = -(0) + b
b = 4
y = -x + 4
Could you please give me brainliest for this? Thanks!
Create two groups of cards with the SAME SUM using as many cards as possible using the numbers 1 2 3 4 5 6 7 8 9
Group 1: 1, 2, 3, 4, 5
Group 2: 6, 7, 8, 9
In this case, the sum of the numbers in Group 1 is 1 + 2 + 3 + 4 + 5 = 15, and the sum of the numbers in Group 2 is 6 + 7 + 8 + 9 = 30. The sum of the numbers in both groups is 15 + 30 = 45, which is the same.
Alternatively, we could create the following two groups:
Group 1: 1, 2, 3, 4
Group 2: 5, 6, 7, 8, 9
In this case, the sum of the numbers in Group 1 is 1 + 2 + 3 + 4 = 10, and the sum of the numbers in Group 2 is 5 + 6 + 7 + 8 + 9 = 35. The sum of the numbers in both groups is 10 + 35 = 45, which is the same.
There are many other ways to create two groups of cards with the same sum using as many cards as possible. The key is to use all of the numbe
Answer:
group 1: 1,2,3,4,5
Group 2: 6,7,8,9
Step-by-step explanation:
my brain
Amy, Brenda and Carleen own a cat, a dog and a fish, but not necessarily in that order. Amy hats cats, and Brenda cannot own a pet with hair because of her allergies. What does Carleen own?
Carleen owns a Dog as her pet.
What is logical thinking?The logical thinking definition is analysing a situation or problem using reason and coming up with potential solutions.
Given that, Amy, Brenda and Carleen own a cat, a dog and a fish, but not necessarily in that order.
It is saying that Amy hats a cat, which ca be meant she has a pet cat
Therefore, Amy owns a pet cat.
Now, Brenda can not have a hairy pet because she has allergic conditions, so the only pet in the given list with no hair is the fish
Therefore, Brenda owns a pet fish.
Now, only Carleen is left, and a pet dog is left.
Therefore, Carleen owns a pet dog.
Hence, Carleen owns a Dog as her pet.
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What is .65 as a fraction?
Simplified
Answer: 0.65=13/20
Step-by-step explanation: First, rewrite the decimal number as a fraction and put 1 in the denominator's place. 0.65/1
Then, multiply to get rid of 2 decimal places. Then, multiply top and bottom by 10^2 which equals 100
0.65/1 × 100/100= 65/100
Find the Greatest Common Factor or GCF of 65 and 100, and reduce the fraction by dividing both the numerator and denominator by GCF = 5,
[tex]\frac{65/5}{100/5}[/tex]=13/20
Hope this helps!
Ava's pet pig is older than Izzy's pet pig, which is 2 years old. Ava adopted her pig when it was 1 year old, and she has had it for 2 years. Help plss
How can 1,000 as an exponential expression with 10 as the base
Answer:
10^3.
Step-by-step explanation:
How can you represent 1,000 as an exponential expression with 10 as the base?
You can represent 1,000 as 10^3. 10 x 10 x 10 = 1000. is read as “10 to the third power” or “10 cubed.”
all numbers are base 10 unless the teacher says to use another base so
there are 3 zeroes so
10^3 is the answer
Hannah is taking out a 8.1% loan to purchase an $15,000 car. The length of the loan is 8 years. How much will she pay in interest?
**WILL MARK BRAINLIEST**
Cell phone Plan A costs $80 per month and comes with a free $630 phone. Cell phone Plan B costs $45 per month but does not come with a phone. If you buy the $630 phone and choose Plan B, how many months is it until your cost is the same as Plan A's? Be sure to:
a) Write an equation to represent the situation where x represents the number of months.
b) Show your work to solve the equation from part a using inverse operations.
c) State the answer.
a) An equation representing the situation where x represents the number of months when Plan A and Plan B cost the same is 80x = 630 + 45x.
b) Using inverse operations, we can state that 80x - 45x = 630 or 35x = 630, and x = 18.
c) From this equation, we determine that x is 18 months.
What is an equation?An equation is a mathematical statement that shows that two or more mathematical expressions are equal or equivalent.
Equations use the equation symbol (=) to depict the equality of the expressions.
Plan A Plan B
Monthly charge $80 $45
Free phone $0 $630
Mathematical Expression:Let Plan A = 0 + 80x
Let Plan B = 630 + 45x
The month the two plans' costs are equal can be derived by equating the two expressions above:
80x = 630 + 45x
80x - 45x = 630
35x = 630
x = 18 months
Thus, solving the equation, we can conclude that choosing Plan B will take 18 months to equal the cost of Plan A and thereafter, be considered cheaper than Plan A.
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If cos(x)= 2/3 and x is in quadrant I, then find exact values for (without solving for x): sin(2x) cos(2x) and tan(2x)
The exact values for sin(2x), cos(2x) and tan(2x) without solving for x 4√5 /9, -1/9 and -4√5 respectively
How to find the exact values for sin(2x) cos(2x) and tan(2x) without solving for x?Given: cos(x)= 2/3 and x is in quadrant IIn trigonometry, cos(x) = adjacent/hypotenuse = 2/3.
adjacent = 2
hypotenuse = 3
Here, we will find the opposite
opposite =√(3²-2²) = √5
sin(x) = (√5)/3 (opp./hyp.)cos(x) = 2/3
(adj./hyp.)tan(x) = (√5)/2 (opp./adj.)
Using trigonometry identity:
sin(2x) = 2sin(x)cos(x) sin(2x)
= 2× (√5)/3 × 2/3sin(2x)
= 4√5 /9cos(2x) = 2cos²(x) - 1
cos(2x) = 2(2/3)² -1cos(2x) = -1/9
Also, we will find the exact value for tan.
tan(2x) = 2tan(x) / 1-tan²(x)tan(2x) = (2(√5))/2 / 1-((√5)/2)²
tan(2x) = √5 / (-1/4)
tan(2x) = -4√5
Therefore, the exact values are given above.
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Question
The product of two consecutive odd integers is 99. Find the integers. Answer only with the positive integers. For example, if
the integers are 8, 10 and -8, -10, then answer 8, 10.
Provide your answer below:
n=
n =
Answer: n= 9 and n=11
Step-by-step explanation:
Assume that x is the lesser of the two numbers. The second figure must be x+2.
Since x*(x+2) = 99, we know that
x^2 + 2x - 99 = 0
We obtain x = 11 and 9 by searching for the roots of this equation.
This can also be resolved in the following ways:
We are aware that the two numbers (x and x +2) are consecutive odd numbers. Since x * (x + 2) = x2 + 2x, the value of x must be near to the square root of 99.
The squares 81 and 100 are the ones closest to the number 99. Additionally, we know that x * (x+2) is bigger than x2 (by a factor of 2x), therefore x must equal 9 and x+2 must equal 11.
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At an art store, 1/4 of
the supplies are for
painting and 13% of the
supplies are for
drawing. What percent
of the supplies are not
for painting or
drawing?
in January the depth of a lake was 943 feet in August the depth of the lake was 754.4 what is the percentage decrease of the depth of the lake from January to August
The percentage decrease of the depth of the lake from January to August is 20%.
What is percentage decrease?The difference between the initial and final numbers is shown as a percentage reduction. It displays a percentage loss of value compared to the original regardless of the units. The decrease is equal to the initial amount less the final amount.
Given,
The depth of lake in January = 943 feet
The depth of lake in August = 754.4 feet
The difference is = (943-754.4) feet
= 186.6 feet
So, the percentage decrease of the depth of the lake from January to August will be = (186.6 ÷ 943) × 100
= 20%
Therefore, the answer is 20%.
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If angle 1 is 25 degrees in the parallelogram pictured above, what is angle 2
The unknown angle in the parallelogram is as follows:
∠2 = 155 degrees.How to find angles of a parallelogram?A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
In other words, a parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other. Opposite sides are equal in length. Opposite angles are equal. The sum of any two adjacent angles of a parallelogram is equal to 180°
The sum of angles in a parallelogram is 360 degrees.
Therefore,
∠1 = 25 degrees
Hence,
Adjacent angles in a parallelogram are supplementary. This means adjacent angles sum up to 180 degrees.
Therefore,
∠2 + ∠1 = 180
∠2 + 25 = 180
∠2 = 180 - 25
∠2 = 155 degrees
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5) a real estate agent bought two triangular 'kittitas' having a common side as shown in the figure from two people for rs 20,00,000 altogether. if he immediately sold the land in the shape of à quadrilateral at rs 15,00,000 per kattha, find his profit or loss.(1 kattha= 338.63 sq. m)
The information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.
How to calculate the profit?From the information given, it was stated that the real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 2000,000 altogether.
It was further depicted that he sold the land in the shape of a quadrilateral at Rs 1,500,000. In their case, the sale is less than the cost and therefore, there's a loss.
The loss will be:
= 2,000,000 - 1,500,000
= 500,000
Therefore, the information illustrated a loss of RS 500,000.
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Complete question
Mr. Gosain?(1 Aana = 31.8 m²) b) A real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 20,00,000 altogether. If he immediately sold the land in the shape of a quadrilateral at Rs 15,00,000 per Kattha, find his profit or loss.(1 Kattha= 338.63 sq. m) danta Excel in Mathematics - Book 9 86 36 m Approved by Curriculum Development Cen 20 m 29 m 25 m 21 m aktapur
A
Choose the correct symbol to
compare these numbers.
-42 [?] -19
=
B
C
V
Answer:
<
Step-by-step explanation:
On a number line, -42 is to the left of -19.
When you compare two numbers on a number line, the number to the left is smaller.
-42 is less than -19
-42 < -19
Solve the triangle using the Law of Sines. (Assume b and c = 20, and ∠C = 63°. Round the length to two decimal places.)
Answer:
a = 16.51
angle A = 54
angle B = 63
Step-by-step explanation:
Recall the law of sines:
sinA/a = sinB/b = sinC/c
We know c is 20, and angle C is 63. Since b is also 20, angle B must also be 20. We know have two of the 3 angles, summing to 126, and we can find the last angle from that. 180-126=54, so angle A must be 54.
To solve for a, we need to know the ratio of the other two terms. Sin(63) is around 0.99, and 0.99/20 is 0.049. So we have 0.049=sin(54)/a. To solve for a, we divide by sin(54) and take the reciprocal of both sides, giving a = (sin54)/0.049, which is about 16.51, which is the length of the side a.
Two sisters are painting mugs. The younger sister can paint 2 mugs every half hour. The older sister can paint 6 mugs every hour. How long will it take the two sisters to paint 80 mugs?
The time it would take the two sisters to paint 80 mugs is 8 hours.
Calculating the time it would take to paint mugsFrom the question, we are to determine how long it would take the sisters to paint 80 mugs
From the given information,
"The younger sister can paint 2 mugs every half hour"
That is,
The younger sister can paint 4 mugs every hour
Also
"The older sister can paint 6 mugs every hour?"
Let x represent the number of hours it would take them to paint 80 mugs.
Then, we can write that
4x + 6x = 80
10x = 80
x = 80/10
x = 8
Hence, the time it would take is 8 hours
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Karl earns $11.20/hr. How much will he be paid this week?
Answer:11.20*168=$1 881.6
Step-by-step explanation: