Use the six steps in the "Blueprint for Problem Solving" to solve the following word problem. You may recognize the solution by just reading the problem. Use n as the variable for the number and write the equation used to describe the problem.When 8 is subtracted from three times a number, the result is 4. Find the number.Equation: ? The number is ? .
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Let n be the number we don't know.
Three times this number can be express as:
[tex]3n[/tex]The sentence "When 8 is subtracted from three times a number" can be express (using the expression we found before) as:
[tex]3n-8[/tex]Finally we know that this is equal to 4, then we have the equation:
[tex]3n-8=4[/tex]Solving for n we have:
[tex]\begin{gathered} 3n-8=4 \\ 3n=8+4 \\ 3n=12 \\ n=\frac{12}{3} \\ n=4 \end{gathered}[/tex]Therefore the number we are looking for is 4.
Related Questions
Jack has $205 and he is spending $2 each day. Which algebraic expression describes this situation, where d represents the number of days?
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M= 205 - 2d
1) We can write a mathematical sentence for that situation, considering Jack's initial amount of money: $205 and the fact that we don't know the number of days (d). But we do know that each day costs Jack $2, i.e. minus 2 dollars per day.
2) Therefore, we can write out the following:
[tex]M_{}=205-2d[/tex]Where M stands for Jack's money and "d" stands for the number of days.
3) Hence the answer is
M= 205 - 2d
6. A basketball coach purchases bananas for the players on his team. Thetable shows total price in dollars. P. of n bananas. Which equation couldrepresent the total price in dollars for n bananas?number of bananastotal price in dollars74.13B47295.31105.90O P = 0.596O P = 5.90-0.59O P = 590//O Pan0.59
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,Given the table of values we can find the equation that will represent the total price in dollars for the bannana by using the equation of a line.
Explanation
The equation of a line is given as
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]We can then remodel the equation above to fit the given table of values. This would give;
[tex]\frac{p_2-p_1}{n_2-n_1}=\frac{p-p_1}{n-n_1}[/tex]Next, we will pick some random points to represent the variables in the equation
[tex]\begin{gathered} p_1=4.13;p_2=4.72 \\ n_1=7;n_2=8 \end{gathered}[/tex]Then we insert the variables into the formula.
[tex]\begin{gathered} \frac{4.72-4.13}{8-7}=\frac{p-4.13}{n-7} \\ \frac{0.59}{1}=\frac{p-4.13}{n-7} \\ p-4.13=0.59(n-7) \\ p-4.13=0.59n-4.13 \\ p=0.59n+4.13-4.13 \\ p=0.59n \end{gathered}[/tex]Answer: The equation is given as p = 0.59n
Figure WXYZ is a rhombus.
Complete the statements below about angle X and angle Y.
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x + z = 180 (Because it is a Rhombus and angles across from each other equal 180)
x = 97
y = 83
one to the sixth power
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sixth power is the exponent of 1.
To obtain the result, multiply 1 by itself 6 times:
1x1x1x1x1x1=1
1^6 = 1
Darnell is running a short experiment on probability. He chooses one block at random from each of the two groups shown below. What is the probabilitythat he will choose a Z from Group 1 and a T from Group 2?
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Answer
P(Z and T)= 8/121
Explanation
The total out come in group 1 = 11
The number of z = 4
Probability of picking a Z in group 1 = 4 / 11
Group 2
The total out comes = 11
Number of T outcomes = 2
Probability of picking a T = 2/11
Therefore, P( Z and T) = P(Z) x P(T)
P(Z and T) = P(Z) x P(T)
P(Z) = 4/11
P(T) = 2/11
P(Z and T) = 4/11 x 2/11
P(z and T) = 8/121
Therefore, the probability of picking a Z and aT is 8/121
Solve the following system of equations. How many solutions are there? x + y = 2 5x + 5y = 10 a) There is no solution. b) There are infinite solutions. c) There is one solution.
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we are given the following system of equations:
[tex]\begin{gathered} x+y=2,\text{ (1)} \\ 5x+5y=10,\text{ (2)} \end{gathered}[/tex]Equation (2) can be rewritten dividing by 5 on both sides as:
[tex]\frac{5x}{5}+\frac{5y}{5}=\frac{10}{5}[/tex]Solving the operations:
[tex]x+y=2,\text{ (2)}[/tex]Since equation (2) is the same equation as equation(1), this means that the system has infinite solutions.
Change 0.005 to equivalent fraction. ANS. _________.
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You can identify that the following is a Decimal number:
[tex]0.005[/tex]In order to convert a Decimal number to an Equivalent fraction, you can follow the steps shown below:
1. You need to write the Decimal number 0.005 as the numerator of the fraction and the denominator must be 1:
[tex]=\frac{0.005}{1}[/tex]2. Now you can multiply the numerator and the denominator by 1,000, in order to remove the decimal places of the numerator (notice that it has three decimal places):
[tex]=\frac{0.005\cdot1,000}{1\cdot1,000}=\frac{5}{1,000}[/tex]3. Finally, you have to reduce the fraction. Notice that you can divide the numerator and the denominator by 5. Then, you get:
[tex]=\frac{1}{200}[/tex]The answer is:
[tex]\frac{1}{200}[/tex]The original price of a pair ofjeans was $40. The price wasmarked down to $35. What is thepercent of decrease in the price?
Answers
SOLUTION
From the question, the original price of the jeans was $40, then the price was reduced to $35. Decrease in price becomes
[tex]40-35=5\text{ dollars }[/tex]Percent decrease becomes
[tex]\begin{gathered} =\frac{decrease\text{ in price}}{original\text{ price}}\times100 \\ =\frac{5}{40}\times100 \\ =\frac{1}{8}\times100 \\ =12.5 \end{gathered}[/tex]hence the answer is 12.5%
The function fx) = 110(1.004)* models the population of rabbits, inthousands, in a state x years after 1990. What is the approximatepopulation of the rabbits in 2012?A 115,000aora8. 120,000Input ->-1990C 310,085,000aayo338,550,000TE
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The following function models the population of rabbits, in thousands, in a state x years after 1990.
[tex]f(x)=110\cdot(1.004)^x[/tex]What is the approximate population of rabbits in 2012?
Count the number of years after 1990 to 2012.
That's 22 years so we have x = 22
Let us substitute x = 22 into the above function
[tex]\begin{gathered} f(22)=110\cdot(1.004)^{22} \\ f(22)=110\cdot(1.091796) \\ f(22)=120.09756 \end{gathered}[/tex]That is approximately 120 thousands or 120,000
Which of the following choices best describes the expression 2/3 (3/4x - 3/2)A: equivalent to 1/2x - 1B: equivalent to x - 1/2C: not equivalent to 1/2x - 1 or x - 1/2
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distributing:
[tex]\begin{gathered} \frac{2}{3}\cdot\frac{3}{4}x-\frac{2}{3}\cdot\frac{3}{2}= \\ =\frac{1}{2}x-1 \end{gathered}[/tex]the expression is equivalent to 1/2x - 1
Using the data above, how many people would be expected to live in Japan if the proportion of people to square miles were the same in Japan as in the United States?
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mason used a 30% coupon to buy a new computer. after the discount, the cost of the computer was $728. determine the original price of the computer . show your work . calculate how much money Mason saved by using the coupon . show your work .
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Let's call x to the original price.
Given that Mason used a 30% coupon, then he paid 0.3x dollars less.
After the discount, the cost of the computer was $728, then
x - 0.3x = 728
0.7x = 728
x = 728/0.7
x = 1040
The original price of the computer was $1040
Mason saves 30% of $1040, which is computed as follows:
[tex]1040\cdot\frac{30}{100}=312[/tex]Mason saves $312
Donna earns a commission. She makes 3.5% of the amount she sells. Yesterday she sold a $800 recliner. How much was her commission.
Answers
Amount sold = $800
Commission = 3.5%
To calculate the commission amount, multiply $800 by the commission percentage in decimal form (divided by 100)
800 x (3.5/100)= 800 x 0.035 = $28
1.question The preimage was(-3, 4) and after the rotation the image was (3, -4). What many degrees counterclockwise did the point rotate?a) 90b) 270c) none aboved) 1802. question
Answers
Answer:
Question 1
d) 180
Question 2:
b T <8, 14>
Explanation:
Here is a graph of the two points.
As can be seen, the two points are on the opposite sides of teacher other, meaning the point (-3,4) has to rotate 180 degrees to get to (3, -4) and vice versa.
Question 2
The coordinates of A and B are
A = (5, 6)
B = (-3, -8 )
If we want to go from B to A, we need to add 8 to the x-coordinate and 14 to the y-coordinate.
Therefore, the translation
[tex]B\rightarrow A\text{ is T<8,14>}[/tex]
If the factors of a polynomial are x-4 and x-5, which value of x make that polynomial 0?
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Given a polynomial of factors below,
[tex]f(x)=(x-4)(x-5)[/tex]To find the values of x at f(x) = 0, substitute for f(x) into the equation above,
[tex]\begin{gathered} (x-4)(x-5)=0 \\ x-4=0 \\ x=4 \\ x-5=0 \\ x=5 \\ x=4\text{ and 5} \end{gathered}[/tex]C is the right option
Drag the tiles to the boxes to form correct pairs.
Answers
Given that
The vertices of the polygon ABCD are A(1,1), B(2,3), C(3,2), and D(2,1). ANd it is reflected about the x-axis.
So we have to find the vertices of the polygon A'B'C'D'.
Explanation -
Since the reflection is about the x-axis, the x-axis will be unchanged and the y-axis will be changed.(sign will be changed)
And it will be changed by the factor +2 in upwards directions.
So if A, B, C, D are reflected across x-axis.
The new points will be A' = (1,-1)
B' = (2,-3)
C' = (3,-2)
D' = (2,-1)
Now we have to add 2 in the y axis as they move upwards.
Then, the required points will be
A' = (1, -1+2) = (1,1)B' = (2, -3+2) = (2,-1)C' = (3,-2+2) = (3,0)D' = (2, -1+2) = (2,1)So these are the required answers.
What is the Center and radius of x2+67+y2=8y+20x
Answers
Let's rewrite the expression as:
[tex]\begin{gathered} x^2+67+y^2-8y-20x=0 \\ so\colon \\ (x-10)^2+(y-4)^2-49=0 \\ (x-10)^2+(y-4)^2=49 \end{gathered}[/tex]Which is the standard equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h,k) is the coordinates of center of the circle and r is the radius
Therefore, the center is:
[tex]\begin{gathered} (h,k)=(10,4) \\ \end{gathered}[/tex]And the radius is:
[tex]r=\sqrt[]{49}=7[/tex]If a normally distributed data set has a mean of81 and a standard deviation of 6, which of thefollowing represents approximately 95% of thedata?
Answers
95% of the data is represented as 69 to 93 (option G)
Explanation:Given:
mean of data = 81
standard deviation = 6
To find:
The option that represents 95% of the data
To determine the right option, we will apply the empirical rule (68-95-99.7%):
68% of the data will fall within 1 standard deviation
95% of the data will fall within 2 standard deviation
99.5% of the data will fall within 3 standard deviation
[tex]\begin{gathered} 2\text{ standard deviation is represented as:} \\ \mu\text{ }\pm\text{ 2\sigma} \\ where\text{ \mu = mean, \sigma = standard deviation} \end{gathered}[/tex]substitute the values:
[tex]\begin{gathered} μ\pm2σ\text{ = 81 }\pm\text{ 2\lparen6\rparen} \\ =\text{ 81 }\pm\text{ 12} \\ 81\text{ }\pm\text{ 12 means 81 - 12 , 81 + 12} \\ =\text{ 69, 93} \\ This\text{ means 95\% of the data is represented from 69 to 93 \lparen option G\rparen} \end{gathered}[/tex]In 2 years, Ariel wants to buy a bicycle that costs 1,000.00. If she opens a savings account that earns 9%interest compounded quarterly, how much will she have to deposit as principal to have enough money in 2 years to buy the bike?
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Let's first list down the information given in the scenario:
a.) In 2 years ariel wants to buy a bicycle that costs 1,000.00
b.) She opens a savings account that earns 9% interest compounded quarterly
Question: How much will she have to deposit as principal to have enough money in 2 years to buy the bike?
To be able to determine the principal amount Ariel will need to deposit, let's use this formula for Compound Interest:
[tex]\text{ A = }P(1\text{ + }\frac{\frac{r}{n}}{100})^{nt}[/tex]Where:
A = Is the final amount/ cost of the bicycle = 1,000
n = Number of times the interest is being compounded = 4
r = Interest rate = 9%
t = No. of periods elapsed/ No. years the principal money be deposited
P = Principal amount/ amount to be deposited
Let's now find the principal amount:
[tex]\text{ A = }P(1\text{ + }\frac{\frac{4}{n}}{100})^{nt}\text{ }\rightarrow\text{ 1,000 = }P(1\text{ + }\frac{\frac{9}{4}}{100})^{4(2)}[/tex][tex]\text{1,000 = }P(1\text{ + }\frac{2.25}{100})^8\text{ }\rightarrow\text{ 1,000 = }P(1\text{ + }0.0225)^8\text{ }\rightarrow1,000=P(1.0225)^8[/tex][tex]\text{ P = }\frac{1,000}{(1.0225)^8}\rightarrow\text{ P = }\frac{1,000}{1.19483114181}[/tex][tex]\text{ P = 836.93835 }\cong\text{ 836.94}[/tex]Therefore, Ariel must deposit a principal amount of 836.94 for her to be able to buy the bike in 2 years.
11 Jamal has a sudden medical emergency, and although his doctors do not agree, he is sure that it was caused by an antibiotic he took to prepare for a tooth extraction. Jamal posts a picture of himself in the hospital on his social media with the hashtag #antibioticskill. Although hashtags can raise awareness of important issues, what might happen if Jamal’s post were to go viral? A. People could be influenced into groupthink and reject antibiotics without knowing the facts. B. People would be encouraged to research the side effects that antibiotics cause before accepting them. C. Jamal would be investigated for making unfounded claims about a product online. D. Jamal could cause people to be more willing to listen to their doctor’s advice.
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Answer:
A.
Step-by-step explanation:
A. People could be influenced into groupthink and reject antibiotics without knowing the facts.
Use elimination to solve eachsystem of equations3x - y = -56x - 2y = 8
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Solution
We are given the pair of simultaneous equation
[tex]\begin{gathered} 3x-y=-5\ldots\ldots\ldots\ldots\ldots(1) \\ 6x-2y=8\ldots\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]we solve using elimination method
equation (1) x 2
[tex]\begin{gathered} 6x-2y=-10\ldots\ldots\ldots\ldots\ldots(1) \\ 6x-2y=8\ldots\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]Equation (2) - equation (1)
We have
[tex]\begin{gathered} (6x-6x)+(-2y+2y)=8-(-10) \\ 0=18 \end{gathered}[/tex]Which is impossible because 0 (zero) can never be equal to 18
Therefore, the simultaneous is not consistent or it degenerate and thus, there is no solution
If logx = -5, what is x?A. -0.00001B. 0.00001C. 0.00005D. -0.00005
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Hello there. To solve this question, we have to remember some properties about logarithms.
Given the logarithmic equation:
[tex]\log(x)=-5[/tex]We want to determine the value of x.
For this, remember the following rule:
[tex]\text{ For }a,\,b\in\mathbb{R}^+\text{ and }b\cancel{=}1,\text{ }\log_b(a)=c\Rightarrow a=b^c[/tex]Such that, in this case, the logarithm has base 10, therefore
[tex]x=10^{-5}[/tex]This power of 10 can be easily found :
[tex]x=0.00001[/tex]It has 5 digits after the decimal place, being the fifth digit a 1.
This is the answer contained in the option B.
The results of an experiment that Lacey is doing are recorded in the table below.Day Number of Amoeba1 2^1 2. 2^23 2^3How many amoebas will be present on the fourth day?216, 6, 46 and 4 are different answers.
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This problem is about geometric sequence, which is a sequence formed by multiplying (or dividing) a constant factor.
In this case, we can observe that each new day has greater power, specifically, its exponent increases by one. This is because each day, the number of amoebas increases by a multiplying factor of 2.
Having said that, we can deduct that the fourth day is going to have a power with exponent 4, because as we said before, each day the exponent increases by 1.
So, the power of the fourth day is
[tex]2^4=16[/tex]Therefore, the right answer is 16, the last choice.Rewrite the following equation y - 7 = -4(x + 1)
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i gave away 10% of my summer job earnings. If i give away $256, how much did i earn over the summer?
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ok
$256 --------------------------- 10%
x --------------------------100%
x = (100 x 256) / 10
x = 25600 / 10
x = $2560
I earned $2560 over the summer
find the value 24÷(1 to the 5th power+5)
Answers
Given
[tex]\frac{24}{(1^5+5)}[/tex]When you power a number by a determined exponent "n" it means that you are multiplying said number n-times by itself. We know that if you multiply 1 by 1 the result is 1, no matter how many times you do it, then 1 multiplied 5 times by itself is also equal to 1:
[tex]1^5=1\cdot1\cdot1\cdot1\cdot1=1[/tex]Then, you can write the calculation as:
[tex]\frac{24}{(1+5)}[/tex]Solve the addition in the denominator's place and then solve the division
[tex]\frac{24}{6}=4[/tex]The result of the calculation is 4
which of the following equations has only one solution? x^2 - 8x + 16 = 0x ( x - 1 ) = 8 x^2 = 16
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Simplify the equation x^2 - 8x + 16 = 0 to obtain the value of x.
[tex]\begin{gathered} x^2-8x+16=0 \\ x^2-2\cdot4\cdot x+(4)^2=0 \\ (x-4)^2=0 \\ (x-4)(x-4)=0 \\ x=4 \end{gathered}[/tex]Equation has one solution, x = 4.
Simplify the equation x ( x - 1 ) = 8 to obtain the value of x.
[tex]\begin{gathered} x(x-1)=8 \\ x^2-x-8=0 \end{gathered}[/tex]This is a quadratic equation which is not a perfect square so it has two solutions.
Simplify the equation x^2 = 16 to obtain the value of x.
[tex]\begin{gathered} x^2=16 \\ x=\sqrt[]{16} \\ =\pm4 \end{gathered}[/tex]Thes equation has two solution x = 4 and x = -4.
So equation x^2 - 8x + 16 = 0 has only one solution and remaining equation has two solutions.
Decide whether enough information is given to prove that △RSV≅△UTV. If so, state the theorem you would use.
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In the diagram we are given that angle S = angle T
We are given that side SV = side TV
We know that vertical angles are equal so angle RVT = angle UVT
WE have 2 angles and the included side so we can use the ASA Congruence theorem which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
There is enough information to use the ASA Congruence Theorem.
The quotient of forty three abs a number m
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Explanations:
Answer:
how many 3/8 are in 3
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We can see that there are 24/8 in 3 units, so we have then that there are 8 times 3/8 in 3 units.
So, the answer is there are 8 times.