The graph of the function f(x) = (x − 3)(x + 1) is shown.
Which describes all of the values for which the graph is positive and decreasing?
A.all real values of x where x < −1
B.all real values of x where x < 1
C.all real values of x where 1 < x < 3
D.all real values of x where x > 3
Answer:
The correct option is A.
Step-by-step explanation:
The given function is
[tex]f(x)=(x-3)(x+1)[/tex]
Equate f(x)=0 to find the x-intercepts of the function.
[tex]0=(x-3)(x+1)[/tex]
[tex]x=3,-1[/tex]
The x-intercepts of the function are -1 and 3. From the below graph it is clear that,
In x<-1, the function is positive and decreasing.
In -1<x<1, the function is negative and decreasing.
In 1<x<3, the function is negative and increasing.
In x>3, the function is positive and increasing.
Therefore the correct option is A.
Cory earns $9 per hour working at the local library. If she works 5 hours on Saturday how much money will she earn?
Find the probability and interpret the results. if convenient, use technology to find the probability. during a certain week the mean price of gasoline was $2.715 per gallon. a random sample of 32 gas stations is drawn from this population. what is the probability that the mean price for the sample was between $2.691 and $2.732 that week? assume sigmaσequals=$0.049
To find the probability of the sample mean price being between $2.691 and $2.732, calculate the Z-scores for each bound and use a Z-table or statistical software. This utilizes the central limit theorem and the concept of Z-scores in statistics.
Explanation:The question is about finding the probability that the mean price for a sample of 32 gas stations was between $2.691 and $2.732, assuming the population mean was $2.715 and standard deviation was $0.049. To solve this, we use the Z-score formula for each sample mean, Z = (X - μ) / (σ/√n), where μ is the population mean, σ is the population standard deviation, and n is the sample size. Then, we find the area between these Z-scores using a Z-table or statistical software to get the probability.
To calculate:
For $2.691: Z = ($2.691 - $2.715) / ($0.049/√32) = -3.44For $2.732: Z = ($2.732 - $2.715) / ($0.049/√32) = 2.45Refer to a Z-table or software with these Z-scores to find the probability of the sample mean price being between $2.691 and $2.732. This method exemplifies how statisticians use Z-scores and the central limit theorem to estimate probabilities relating to sample means.
the vertex of this parabola is at (3,5). When the y-value is 6, the x-value is -1. What is the coefficient of the squared term in the parabolas equation
The coefficient of the squared term in the parabola's equation, with a vertex at (3,5) and passing through the point (-1,6), is 1/16.
The student is asking about the coefficient of the squared term in the parabola's equation given that the vertex is at (3,5) and another point on the parabola is (-1,6). Since we know the vertex, we can write the vertex form of a parabolic equation as:
y = a(x - h)
^2 + k
Plugging the vertex into the equation, we get:
5 = a(3 - 3)
^2 + 5
This simplifies down to:
5 = a(0) + 5
So, we cannot determine 'a' from the vertex alone. However, we can use the other point to find 'a'. Plugging the coordinates (-1,6) into the vertex form, we get:
6 = a(-1 - 3)^2 + 5
6 = a(-4)^2 + 5
6 = 16a + 5
1 = 16a
a = 1/16
Therefore, the coefficient 'a' is 1/16.
186.302 in expanded form
what do Subway fraction and a whole number it is 5/6 x 36
Which is another way to name UST? TSR TSU USR UTS
A given line has the equation 10x + 2y = −2.
Answer:
5x+y=12
Step-by-step explanation:
Which equation has a y-intercept of 0?
A) y = 7x + 1
B) y = -3x
C) y = 4x - 4
D) y = x + 5
One pound of grapes costs $1.55. Which equation correctly shows a pair of equivalent ratios that can be used to find the cost of 3.5 pounds of grapes?
A First one
B second one
C third one
D last one
Answer:
A
Step-by-step explanation:
One pound of grapes costs $1.55. To find the amount x of 3.5 pounds of grapes we would have to multiply 1.55 by 3.5. This would give us the amount x we would have to pay for them.
If we examine the 4 equivalent radios shown in the pictures, we will see that the first one correctly shows this equivalency.
[tex]\frac{1.55}{1} = \frac{x}{3.5}[/tex]
The other 3 pictures show radios that would give us x = 3.5 / 1.55 (second and third) or x = 1.55 / 3.5 (fourth picture).
Therefore, the correct answer would be a)
If two lines are perpendicular, which statement must be true? A.The slopes of the two lines are equal. B.The slopes of the two lines are undefined. C.The slopes of the two lines are zero. D.The slopes of the two lines are negative reciprocals.
Answer:
Option D is correct that is The Slopes of two lines are negative reciprocals.
Step-by-step explanation:
Perpendicular lines are the lines which intersect each other at right angle or make 90° angle with each other.
we that the Slope of perpendicular lines are equal to -1
Therefore, Option D is correct that is The Slopes of two lines are negative reciprocals.
Answer:
The answer to your question is D. The slopes of the two lines are negative reciprocals.
Step-by-step explanation:
Hope this helps have a great day :D
How do I answer question #9
which of the following equations represents a direct variation?
A y=x -1
B y=×/3
C y = x + 5
D y = 2x-3
The equation represents a direct variation is y = x/3. So option (b) is correct.
A direct variation is a relationship between two variables where one variable is a constant multiple of the other. To identify a direct variation, we look for equations in the form y = kx, where k is a constant.
Let's analyze each equation:
A) y = x - 1
This equation doesn't represent a direct variation because it includes a constant term (-1) in addition to the variable x.
B) y = x/3
This equation represents a direct variation because it's in the form y = kx, where k = 1/3.
C) y = x + 5
Similar to option A, this equation doesn't represent a direct variation because it includes a constant term (+5) in addition to the variable x.
D) y = 2x - 3
Similar to option A, this equation doesn't represent a direct variation because it includes a constant term (-3) in addition to the variable x.
Therefore, the correct answer is B) y = x/3, as it represents a direct variation.
Andrew believes that the probability that he will win the tennis match is 2/9. what is the probability that he will lose the tennis match?
Ina case whereby Andrew believes that the probability that he will win the tennis match is 2/9.the probability that he will lose the tennis match is [tex]\frac{7}{9}[/tex]
What is probability?Probability is the likelihood that something will occur. When we're not sure how something will turn out, we can discuss the likelihood of different outcomes, or their probabilities. Statistics is the study of events that follow a probability distribution.
p(he will win the tennis match )= 2/9.
P(he will lose the tennis match) =1 - 2/9
[tex]\frac{9}{9} -\frac{2}{9}[/tex]
=[tex]\frac{7}{9}[/tex]
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jeff finds some bugs. he finds 10 fewer grasshoppers than crickets. he finds 5 few crickets than ladybugs. if jeff finds 5 grasshoppers. how many ladybugs does jeff find? how many crickets does he finds?
Jeff found 15 crickets and 20 ladybugs
Let the number of grasshoppers be x
Let the number of crickets be y
Let the number of ladybugs be z
If Jeff finds 10 fewer grasshoppers than crickets, hence x = y - 10
If he finds 5 few crickets than ladybugs, hence y = z - 5
If jeff finds 5 grasshoppers, hence x = 5
Since x = y - 10
5 = y - 10
y = 5 + 10
y = 15
Similarly since y = z - 5
15 = z - 5
z = 15 + 5
z = 20
This shows that Jeff found 15 crickets and 20 ladybugs
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!!!!PLEASE HELP!!!!
Joe purchased a tray of 48 petunias to plant in his garden. The graph shows points representing the number of flowers left to plant at several different times while Joe is planting.
Select from the drop-down menus to complete the equation, in standard form, that represents the relationship between the number of petunias left to plant, y, and the time, x, Joe has spent planting.
Required equation is y - 36 = (24 - 36)/(2 - 1) (x - 1)
y - 36 = -12(x - 1)
y - 36 = -12x + 12
12x + y = 12 + 36
12x + y = 48
Answer:
12x + y = 48
Step-by-step explanation:
Which ordered pairs in the form (x, y) are solutions to the equation 7x−5y=28 ?Solation 7x−5y=28 ? A. (−6, −14) B. (7,9) C. (4,10) D.(-1,-7)
all real numbers that are less than or equal to -27?in interval notation.
The set of all real numbers less than or equal to -27 in interval notation is (-∞, -27].
Explanation:The set of all real numbers that are less than or equal to -27 can be represented in interval notation as (-∞, -27]. In interval notation, a square bracket indicates that the endpoint is included in the set. In this case, -27 is included because the question states 'less than or equal to.' The symbol '-∞' represents negative infinity, indicating that there is no lower bound on the set.
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Jane is saving her money in order to purchase a new racing bike. She initially saves $3 and plans to double the amount she saves each month. The bike Jane wants is $1,536 at the local bike shop.
Which equation represents this situation, and after how many months, t, will Jane have enough money to purchase the bike?
A, 3(2)t = 1,536; t = 11
B, 3(1.2)t = 1,536; t = 35
C, (3 · 2)t = 1,536; t = 9
D, 3(2)t = 1,536; t = 9
Answer:
Hence, option: D is true.
D) 3×(2)^t = 1,536; t = 9
Step-by-step explanation:
Jane is saving her money in order to purchase a new racing bike. She initially saves $3 and plans to double the amount she saves each month.
he bike Jane wants is $1,536 at the local bike shop.
The equation that represents this situation, and after how many months, t, will Jane have enough money to purchase the bike is:
D) 3×(2)^t = 1,536; t = 9
since in the first month the cost is:
[tex]C_1=3\times 2[/tex]
in next month the cost is:
[tex]C_2=3\times 2\times 2\\\\C_2=3\times 2^2[/tex]
in t=3 months the expression is:
[tex]C_3=3\times 2^2\times 2\\\\C_3=3\times 2^3[/tex]
Hence in general we say:
[tex]C_t=3\times 2^t[/tex]
Hence,
[tex]3\times 2^t=1536\\\\2^t=\dfrac{1536}{3}\\\\2^t=512\\\\2^t=2^9\\\\t=9[/tex]
Hence, option: D is true.
D) 3×(2)^t = 1,536; t = 9
I need help fast!! Having trouble with this!!
THE ANSWER TO THIS PROMBLEM IS A
Sharon earns $25 per item she sells plis a base salary of $100 per week. Write and solve an inequality to finfmd how many items she must selll to earn at least $700per week.
Donna opens a certificate of deposit (CD) with $2,000. The bank offers a 3% interest rate. If the account compounds quarterly, which of the following equations represents the future value of the account, after 1 year?
What is the constant of proportionality I. The equation y=5x?
Answer:
The value of the constant of proportionality is [tex]k=5[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
The value of the constant k is equal to the value of the slope
In this problem we have
[tex]y=5x[/tex] ------> is a linear direct variation
The slope is [tex]m=5[/tex]
therefore
The value of the constant of proportionality is [tex]k=5[/tex]
The constant of proportionality on the equation is 5.
To obtain the constant of proportionality ;
We compare the general direct proportionality relation with the equation given. The equation given : y = 5xThe direct relationship between y and x is :
y α x
y = kx - - - (1)
Where, y and x are variables and k is the constant of proportionality.
Comparing equation (1) with the equation given :
y = kx
y = 5x
We can observe that, k in the equation (1) equals to 5 in the given equation.
Hence, the constant of proportionality is 5
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A group of friends is collecting aluminum for a recycling drive.Each person who donates at least 4.25 pounds of aluminum receives a free movie coupon.The weight of each person's donation is shown in the table.
A. order the weights of the donations from greatest to least.
B. Which of the friends will receive a free movie coupon? Which will not?
C.What if? Would the person with the smallest donation win a movie coupon if he or she had collected 1/2 pound more of aluminum? Explain
Brenda. Claire Jim. Micah
4.3. 5.5. 6 1/6. 15/4
Peter
4 3/8
Answer:
Brenda Claire Jim Micah Peter
4.3 5.5 6 1/6 15/4 4 3/8
4.3 5.5 6.17 3.75 4.375 (all values in decimal)
A. order the weights of the donations from greatest to least.
6.17 , 5.5 , 4.375 , 4.3 , 3.75
B. Which of the friends will receive a free movie coupon? Which will not?
As given - Each person who donates at least 4.25 pounds of aluminum receives a free movie coupon.
So, Brenda, Claire, Jim and Peter will receive coupons and Micah will not receive.
C.What if? Would the person with the smallest donation win a movie coupon if he or she had collected 1/2 pound more of aluminum?
Micah got 3.75 pounds and if he got 0.5 pounds more, then he would have;
[tex]3.75+0.5=4.25[/tex] pounds
Then he would have got the coupon as a minimum of 4.25 pounds is required.
A company borrowed $25,000 at 3.5% and was charged $2,625 in interest. How long was it before the company repaid the money?
Answer-
The company repaid the money in 3 years.
Solution-
A company borrowed $25,000 at 3.5% and was charged $2,625 in interest.
Considering the interest as simple interest,
[tex]\text{interset}=\dfrac{\text{Principal}\cdot \text{Rate of interest}\cdot \text{Time period}}{100}[/tex]
Here,
Interest = $2625
Principal = $25000
Rate of interest = 3.5% annually
Putting the values,
[tex]\Rightarrow 2625=\dfrac{25000\times 3.5\times t}{100}[/tex]
[tex]\Rightarrow t=\dfrac{2625\times 100}{25000\times 3.5}[/tex]
[tex]\Rightarrow t=3\ years[/tex]
Therefore, the company repaid the money in 3 years.
Find the inverse laplace transform of the function by using the convolution theorem. f(s) = 1 s5(s2 + 1)
A business bought a lot of 2,500 lamps for fifty thousand dollars and wants to to sell them at 15% prfit. How much should each lamp cost?
explain -3 1/3, 3.3, -3 and 3/4, 3.5 from least to greatest
If y has moment-generating function m(t) = e 6(e t −1) , what is p(|y − µ| ≤ 2σ)?
Geneva rode her bike a total of 2 1/2 miles from her house to school. First she rode 4/5 mile from her house to the park. Then she rode 1/5 mile from the park to her friends house . Finally she rode the rest of the way to her school? How many miles did she ride from her friends house to school
Answer:
She rode [tex]1\frac{1}{2}[/tex] miles from her friends house to school.
Step-by-step explanation:
Geneva rode her bike a total = [tex]2\frac{1}{2}[/tex] miles
She rode from her house to the park = [tex]\frac{4}{5}[/tex] miles
She rode from the park to her friend's house = [tex]\frac{1}{5}[/tex] miles
total distance from her house to her friend's house = [tex]\frac{4}{5}+\frac{1}{5}[/tex] = 1 mile
Finally she rode the rest of the way to her school.
distance between her friend's house to school = [tex]2\frac{1}{2}-1[/tex] = [tex]\frac{3}{2}[/tex] miles
[tex]1\frac{1}{2}[/tex] miles she rode from her friends house to school