Answer: The correct answer is x=−3 or x=5
Step-by-step explanation:
Solve for x^2−2x=15 using the quadratic equation
Step 1) Subtract 15 from both sides
x2−2x−15=15−15
x2−2x−15=0
For this equation: a=1, b=-2, c=-15
1x2+−2x+−15=0
Step 2) Use quadratic formula with a=1, b=-2, c=-15
x= (−b±√b2−4ac)/2a
x= (−(−2)±√(−2)2−4(1)(−15))/2(1)
x= (2±√64)/2
x=5 or x=−3
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The state board of education has $5,647 to buy new calculators. each calculator costs $2. after buying as many calculators as it can with its budget, how much money will the state board of education have left over?
By basic arithmetic, the state board of education will have $1 left .
What is meant by basic arithmetic?The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.
Addition, subtraction, multiplication, and division are the four operations employed in arithmetic.
The total amount the state board has = $5647
The cost of calculator = $ 2
The total number of calculators bought = 5647/2
= 2323.5
≈ 2823
So, the cost of 2323 calculators
= 2823 × 2
= 5646
So, the money the state board of education left = $5647 - $5646
= $1
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List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
The reduced fraction is 6/7 using GCF method.
What is GCF method?
The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)
Given,
the fraction = 24/28.
the factors of 24 = 2×2×2×3
The factors of 28 = 2×2×7
The gcf is 2 × 2 = 4
divide the denominator and numerator by 4
24 ÷ 4 = 6
28÷ 4 = 7
We get,
the fraction = 6/7.
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15÷(3+13)2
A 2
B 5
C p
D 2 over 5
Answer: D.
Step-by-step explanation:
9. A family ordered 2 large pizzas for lunch. They ate
7
-
8
of one pizza and of the other pizza. What
fraction of a pizza was left for dinner?
118
b. 1/2
d. 12/12
b.
e.
318
334
C.
718
00
10
Answer:
9/16
Step-by-step explanation:
Find the initial population size
The numeric values for the population function are given as follows:
Initial population: 49 individuals.Population after eight years: 292 individuals.How to find the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, each instance of the input variable in the function or in the expression is replaced by the value at which we want to find the numeric value.
The function giving the population after t years is defined as follows:
[tex]P(t) = \frac{340}{1 + 6e^{-0.45t}}[/tex]
The initial population is the numeric value at t = 0, that is, the lone instance of t is replaced by zero, hence:
[tex]P(0) = \frac{340}{1 + 6e^{-0.45(0)}} = \frac{340}{7} = 49[/tex]
After eight years, the population is given by the numeric value at t = 8, hence:
[tex]P(8) = \frac{340}{1 + 6e^{-0.45(8)}} = 292[/tex]
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Help please, I don't know how to get QS
The complete proof using the AAS congruence postulate and CPCTC is explained below to show that QT ≅ SR.
What is the AAS Congruence Postulate?When two angles of a triangle, and one of its side that is nonincluded are congruent to corresponding two angles and a nonincluded side in the another triangle, then both triangles are congruent by the AAS congruence postulate.
If two triangles are congruent, then all its corresponding parts are also congruent to each other based on the CPCTC theorem.
Below is the two-column proof that proves that side QT is congruent to side SR.
Statement Reasons
1. ∠R ≅ ∠T, QT ≅ SR 1. Given
2. ∠TQS ≅ ∠RSQ 2. Alternate interior angles
3. QS ≅ QS 3. Reflexive property
4. ΔTQS ≅ ΔRSQ 4. AAS
5. QT ≅ SR 5. CPCTC
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It takes 12 minutes per pound to cook a turkey and dinner is at
3:00 pm.
How many hours and minutes is this?
Answer:
The result is 2 hours
Hope this helped!
PLEASE HELP!!!Which is an equation in point-slope form for the line that passes through the points (−1,4) and (3,−4)?
100 POINTS!!!!!
Answer:
y - 4 = - 2(x + 1)-------------------------
GivenPoints (-1, 4) and (3, - 4)Find the slopem = (- 4 - 4)/(3 - (-1)) = - 8/4 = - 2Use one of the points and the point-slope formy - y₁ = m(x - x₁)y - 4 = - 2(x - (-1)) ⇒ y - 4 = - 2(x + 1)Which equation has the solution x = 9? Select each correct answer 0 +7=8 24-2x = 13 | | 4 + 5x = 18 0¹²-3=6 02x-3 = 15 3x + 2 = 25
HELP PLS!
For x to be a solution, there must be the quantity x in the equation.
All the equations that contain x are :
+) 24 - 2x = 13
+) 4 + 5x = 18
+) 2x - 3 = 15
+) 3x + 2 = 25
We will solve for the value of x for each of the equation :
+) 24 - 2x = 13
-> 2x = 24 - 13 = 11
-> x = 11/2 = 5.5
+) 4 + 5x = 18
-> 5x = 18 - 4 = 14
-> x = 14/5 = 2.8
+) 2x - 3 = 15
-> 2x = 15 + 3 = 18
-> x = 18/2 = 9
+) 3x + 2 = 25
-> 3x = 25 - 2 = 23
-> x = 23/3.
We can see, only the equation 2x-3 = 15 has x=9 as a solution.
PLEASE HELP ASAP express
Answer: 5+3*3(3)-2= 30
Step-by-step explanation: Replacing x with 2 and using PEMDAS
What is the solution to the equation 1/4 ×-1/8=7/8+1/2x? X?
O x=-5
O x=-4
O x = 4
O x = 5
Answer: I think its B: x=-4
Step-by-step explanation:
1/7*5/3 um i need help plese i only have 1 secont
The product of the fractions 1/7*5/3 is 5/21.
The product of the fractions= product of the numerator/product of the denominator.
The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively.
We multiply the 1 and 5, the numerators and 7 and 3 the denominators.
Therefore the product of the fractions is 5/21.
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Answer:
5/21
Step-by-step explanation:
Given problem,
→ (1/7) × (5/3)
Let's solve the problem,
→ (1/7) × (5/3)
→ (1 × 5)/(7 × 3)
→ 5/21
Thus, the answer is 5/21.
a department store chain is expanding into a new market, and is considering 24 different sites on which to locate 6 stores. assuming that each site is equally likely to be chosen, in how many ways can the sites for the new stores be selected? a) 144 b) 96,909,120 c) 168 d) 134,596 e) 30 f) none of the above.
Option b. 96,909,120 is the correct answer. The number of ways in which the new site can be chosen to locate 6 stores in 96,909,120 ways
We can find the number of ways by multiplying the number of possibilities each store can have.
Store 1, can be placed on 24 sites. Store 2 can be placed on 23 sites (since store 1 is already on site 1). Store 3 can be placed on 22 sites. Store 4 can be placed on 21 sites. Store 5 can be placed on 20 sites. Store 6 can be placed on 19 sites
Therefore the number of ways is:
C = 24 * 23 * 22 * 21 * 20 * 19
C = 9,69,09,120 possibilities
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Here is a correlation, does it also represent causation? Explain you answer.
The miles driven and the amount of gasoline used.
Yes the miles driven and the amount of gasoline used can be said to have a causation as well as a correlation.
What is causation in statistics?The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.
There is a causal relationship between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.
When the amount of gasoline is small, it would cause the miles covered to be just a few miles. Or if there is no gas, then no mile would be covered.
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How to identify whether the word problem is about direct proportion, inverse proportion or partitive proportion?
The identification process of direct proportion, inverse proportion and partitive proportion is show below.
What is proportion?Proportion is comparison of things or magnitudes in terms of size, amount.
In direct proportion, when one quantity increase or decreases, the another quantity will also increase or decrease in the same ratio.
In inverse proportion, When one quantity increases, the another quantity decreases and vise versa.
Partitive proportion is when the division of a quantity into two or more equal or unequal parts.
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how do I solve this?
Answer:
7
Step-by-step explanation: -13(-1) + 36 + 42(-1)
Step 1: -13(-1)= 13
Step 2: 13 + 36= 49
Step 3: 49 + 42(-1)= 49 + (-42)= 7
Solution: 7
suppose a sample of thirty 25- to 34-year-olds showed a sample mean of 118.4 texts per day. assume a population standard deviation of 33.17 texts per day. compute the p-value. (round your answer to four decimal places.) p-value
The p-value of the distribution of population standard deviation of 33.17 texts per day is 0.9435
The test statistic's "p-value" measures how likely it is that future results will be at least as extreme as the one your sample yielded. You must understand that the null hypothesis is the underlying presumption to compute this probability.
The parameters are as follows:
The sample mean ([tex]\bar x[/tex]) = 118.4
The population standard deviation ([tex]\sigma[/tex]) = 33.17
The sample size (n) = 30
Calculate the z-score first.
[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }[/tex]
according to the entire question, x = 128
So, we have:
[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{\sqrt{30} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{5.477 } } }\\\\z = \bold{ \frac{9.6}{ 6.056} }\\\\z = 1.5852[/tex]
As determined by the z table of probability, p = 0.9435395
or p = 0.9435 (approx.)
Consequently, the distribution's p-value is 0.9435.
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Samuel is remodeling his basement. One part of the planning involves the flooring. He
knows that he would like both carpet and hardwood but isn't sure how much of each he will
use. The most amount of flooring area he can cover is 2000 square feet. The carpet is $4.50
per square foot, and the hardwood is $8.25 per square foot. Both prices include labor costs.
Samuel has budgeted $10,000 for the flooring.
Write a system of inequalities to represent the maximum amount of flooring needed and
the maximum amount of money Samuel wants to spend.
A system of inequality to represent the maximum amount of flooring needed is c + h ≥ 2000.
A system of inequality to represent the maximum amount of money wants to spend is 4.50c + 8.25h ≥ 10,000.
How to write and solve this inequality?In order to solve this word problem, we would assign variables to the number of square feet of carpet and the number of square feet of hardwood for the given flooring area, and then translate the word problem into an algebraic inequality as follows:
Let the variable c represent the number of square feet of carpet.Let the variable h represent the number of square feet of hardwood.For the maximum amount of flooring needed, we have:
c + h ≥ 2000
For the maximum amount of money, we have:
4.50c + 8.25h ≥ 10,000.
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PLSSSS HELPPP UGRNETLY
The GCF of the number given as 45 and 27 is 9 and the factored expression is 9(5 - 3)
How to determine the GCF of the expressions?From the question, we have the following statement
The greatest common factor of 45 and 27
Rewrite the given expression as follows
This is represented using
45 and 27
Factor out 3 from the expression
So, we have the following representation
15 and 9 => Factored 3
Factor out 3 from the expression
So, we have the following representation
5 and 3 => Factored 3 * 3
So, we have
Factored = 3 * 3 = 9
This represents the GCF
So, the GCF is 9
Factor the expressionIn (a), we have
5 and 3 => Factored 3 * 3
This means that
45 - 27 = 3 * 3(5 - 3)
Evaluate the product
45 - 27 = 9(5 - 3)
Hence, the factored expression is 9(5 - 3)
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what is the probability that at least nine out of 12 cars have an acceptable emissions level? (round your answer to three decimal places.)
The probability that at least nine out of 12 cars have an acceptable emissions level is 0.333.
What is probability?The branch of mathematics which deals with the analysis of random phenomena is called probability. The probability of an event is defined as the ratio of favorable events to the total number of events.
P(E) = F(E)/T(E)
Where P(E) = probability of an event which occur\
F(E) = Number of favorable events
T(E)= Total number of events
Here given that the total number of cars T(E) =12
And the number of cars that have acceptable emissions level F(E) = 4
Hence Probability that at least nine cars have an acceptable emission level
=4/12
= 1/3
= 0.333
The probability that at least nine out of 12 cars have an acceptable emissions level is 0.333.
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10. A life insurance company found that
among its last 200 claims, there were six
dozen smokers. What is the ratio of smokers
to nonsmokers in this group of claimants?
Write in lowest terms.
for homework .
the probability that an individual without a college education earns more than $100,000 is 0.4, whereas the probability that a person with a b.s. or higher degree earns more than $100,000 is 0.6. the probability that a person chosen at random has a b.s. degree is 0.4. what is the probability that a person has at least a b.s. degree if it is known that he or she earns more than $100,000? (round your answer to four decimal places.)
The Probability that someone holds b.s. degree if it is known that he or she earns more than $100,000 is 0.75.
Considering the values given in the question,
P(earns more than $100000 without college education) = 0.2
P(earns more than $100000 with a B.S. or higher degree) = 0.6
P(Has a B.S. degree) = 0.5
P(earns more than $100000) = P(earns more than $100000 | without college education) × P(without college education) + P(earns more than $100000 | with a B.S. or higher degree) × P(has a B.S. degree)
= 0.2 × (1 - 0.5) + 0.6 × 0.5
= 0.4
P(at least a B.S. degree | earns more than $100,000) = P(earns more than $100000 | with a B.S. or higher degree) × P(has a B.S. degree) / P(earns more than $100000)
= 0.6 × 0.5 / 0.4
= 0.75
Therefore, If a person's income above $100,000 is known, there is a 0.75 probability that they have at least a b.s. degree.
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Decide whether each equation is true for all, one, or no values of x.
1. 3x + 9 = -4.5x + 20 ; This is true for one value of x.
2. 9(x + 3) = 9x + 12 ; This is true for no values of x.
3. 4(2x + 3) = 12 + 8x ; True for any values of x.
Given,
The equations;
1. 3x + 9 = -4.5x + 20
2. 9(x + 3) = 9x + 12
3. 4(2x + 3) = 12 + 8x
We have to find whether each equation is true for all, one or no values of x.
Here,
1. 3x + 9 = -4.5x + 20
Solve for x;
3x + 4.5x = 20 - 9
7.5x = 11
x = 11/7.5
x = 1.47
Then,
This is true for one value of x.
2. 9(x + 3) = 9x + 12
Solve using distributive property;
9x + 27 = 9x + 12
9x - 9x = 12 - 27
0 = -15
This is true for no values of x.
3. 4(2x + 3) = 12 + 8x
Use distributive property and solve;
8x + 12 = 12 + 8x
8x - 8x = 12 - 12
0 = 0
True for any values of x.
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Question 2
Which set of rational numbers is arranged from least to greatest?
O
O
O
O
-3.5, 4, 2, 3
11
-3.5, 4,3,2
113
2, 3.
1
4.-3.5
11
4.3.2, -3.5
11
10 pts
Answer:
The second option.
Step-by-step explanation:
We can figure this out by going down each option and checking if it works and is arranged from least to greatest.
The first option provides the numbers -3.5, -1/4, 2, 1/3 in that order.
This does not work because 1/3 is less than 1 which is less than 2. 1/3 should come before 2.
The second option provides the numbers -3.5, -1/4, 1/3, 2.
This option does work, because -3.5 is less than -1/4, -1/4 is less than 1/3 because it is negative, and 1/3 is less than 2.
If we look at this on a number line, the numbers that are smaller will appear farther to the left on the number line.
Write an equation of a line that passes through the point (1, -2) and is parallel to the line y = x - 5.
Answer:
y = x - 3
Step-by-step explanation:
y - y1 = m( x - x1 )
y - (-2) = 1 (x - 1)
y + 2 = x - 1
y = x - 3
By rounding each number to 1 significant figure estimate to 6235.1 x 21.5
By rounding each number to 1 significant figure estimate to 6235.1 x 21.5 is 120000.
How can the numbers be rounded up?The concept of significant fiqure is based on the looking for the first non zero number that is resnt in the numbers , and that will be one significant figure, and it goes like that.
Then let us round each of the given fiqures into 1 significant fiqure as instructed:
6235.1 to 1 significant figure will be 6000 , because 6 is the first significant fiqure and the value that follow 6 is less than 5, it can not been approximated
21.5 to 1 significant figure will be 20
Then (6000*20) =120000
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Teresa estimates that the height of a giraffe in a zoo is 18 feet. In fact, it is 16 feet tall. What is Teresa’s percentage error? Use proportional relationships to solve the problem. Show all your work and round your answer to the nearest tenth.
Answer: 11.1%
Step-by-step explanation:
The formula for percent error is:
|Actual-predicted/predicted| * 100%
In the context of the problem:
Actual = 16 ft
Predicted = 18 ft
Plug these values into the equation:
|16-18/18| * 100% = percent error
11.11% = percent error
If you have any other problems about percent error, you should be able to just plug these values into the formula
The contrapositive of a conditional statement is "If an item is not worth five dimes, then it is not worth two quarters.”
What is the converse of the original statement?
The converse of the statement that says that If an item is not worth five dimes, then it is not worth two quarters is: If an item is worth five dimes it is worth two quarters.
What is the converse of a statement?By swapping the hypothesis and the conclusion, a statement can be made to mean the opposite. "If two lines don't intersect, then they are parallel" is the inverse of "If two lines overlap, then they are parallel." If q, then p is the opposite of "if p, then q."
The converse of a statement may not always have the same truth value as the original. For instance, "All mammals are tigers" is the polar opposite of "All tigers are mammals." This is undoubtedly untrue.
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Weekly
wages at a certain factory
are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$350 and $400.
[ ? ]%
The probability that a worker selected at random makes between $350 and $400 = 0.34134
What is a z score formula?
The standard score represents how far a raw score deviates from or exceeds the mean of the phenomenon being observed or measured. Positive standard scores are assigned to raw scores that are greater than the mean, while negative standard scores are assigned to raw scores that are less than the mean.
By using the z score formula:
z = (x - μ) / σ
Where,
x = raw score
μ = mean
σ = Standard deviation
We are told in the question to find the probability that a worker selected at random makes between $350 and $400
Consider, x1 = 350 and x2= 400 with the mean μ = 400 and standard deviation σ = $50.
z1 = (x1 - μ) / σ = (350-400) / 50 = -1
z2 = (x2 - μ) / σ = (400 - 400) / 50 = (0/50) = 0
From tables, P(z <= -1) = 0.15866
P(z <= 0) = 0.5
Then, the probability would give us, P(-1 ≤ z ≤ 0) =0.5 - 0.15866 = 0.34134
Hence, The probability that a worker selected at random makes between $350 and $400 = 0.34134
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Please help as I am confused
The region common to both the graphs as shown is the solution set.
What are the system of equations?A system of equations is a collection of two or more equations with a same set of unknowns
Given are the following quadratic inequalities -
x² - 6x - 7 < 0
3x² - 28x + 32 ≤ 0
We have the following quadratic inequalities -
x² - 6x - 7 < 0
3x² - 28x + 32 ≤ 0
We will plot both of them. The common region be the possible set of solutions to the given inequalities. Refer to the graph attached. The region common to both the graphs is the solution set.
Therefore, the region common to both the graphs as shown is the solution set.
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