Which of the following graphs shows the solution set for the inequality below?
|x + 2| + 7 > 10
Answers
Work Shown:
|x+2| + 7 > 10
|x+2| > 10-7
|x+2| > 3
x+2 > 3 or x+2 < -3
x > 3-2 or x < -3-2
x > 1 or x < -5
The graph for x > 1 has an open circle at 1 and shading to the right.
The graph for x < -5 has an open circle at -5 and shading to the left
Both of these facts combine to describe Choice C
In other words, we have open circles at -5 and 1, with nearly everything shaded except for the region between the open circles.
The open circles are used to exclude those x values mentioned.
Related Questions
What is the partial fraction decomposition of StartFraction 7 x squared + 14 Over (x squared + 3) squared EndFraction?
Answers
The final decomposition of the given partial fraction is; 7 + (-7/(x² + 3))
How to decompose partial fractions?We are given the polynomial fraction (7x² + 14)/(x² + 3) to decompose.
Now, due to the fact that the degree of the numerator is not less than the degree of the denominator, we will perform polynomial long division to get;
(7x² + 14)/(x² + 3) = 7 + (-7/(x² + 3))
Now, the second term (-7/(x² + 3)) cannot be decomposed further and as such, we say that our final decomposition of the given partial fraction is;
7 + (-7/(x² + 3))
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What is the value for y?
What is the value of x?
Enter your answer in the box.
x =
Equiangular triangle A B C. Angles A, B, and C are marked congruent. The length of side A C is labeled as 5 x minus 22. The length of side A B is labeled as 4 x minus 10. The length of side B C is labeled as 3 x plus 2.
Enter your answer in the box.
y =
An isosceles triangle A B C with horizontal base B C and vertex A is above the base. Side A C and C B are labeled with single tick mark. All the three angles are labeled. Base angles C A B is labeled as 50 degrees and angle C B A is labeled as 2x degrees. The angle A C B is labeled left parenthesis 5 y plus 10 right parenthesis degrees.
Answers
1. The value of x in the equilateral triangle is: 12
2. x = 25; y = 14
What is an Equilateral Triangle?If a triangle has three sides that are marked congruent, then the triangle is an equilateral triangle.
1. Since triangle ABC is an equilateral triangle and its sides are equal, therefore:
5x - 22 = 3x + 2 [congruent sides]
Solve for x
5x - 3x = 22 + 2
2x = 24
2x/2 = 24/2
x = 12
The value of x is: 12.
2. Base angles of an isosceles triangle are congruent, therefore:
2x = 50
x = 50/2
x = 25
Thus, using the triangle sum theorem, we have:
2x + 50 + 5y + 10 = 180
Plug in the value of x and find y
2(25) + 50 + 5y + 10 = 180
50 + 50 + 5y + 10 = 180
110 + 5y = 180
5y = 180 - 110
5y = 70
y = 70/5
y = 14
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Which of the following is NOT a rational expression?
Answers
The expression that is not rational is the first one:
[tex]f(x) = \frac{6x}{4}[/tex]
Which of the given expressions is not rational?A rational expression is something of the form:
[tex]f(x) = \frac{q(x)}{p(x)}[/tex]
Such that q(x) can be any polynomial, and p(x) is a polynomial of at least degree 1.
This means that we need to have the variable "x" on the denominator.
Then is easy to recognize the expression that is not rational, is the one that does not have x on the denominator, which is the first one:
[tex]f(x) = \frac{6x}{4}[/tex]
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Answer: B
Step-by-step explanation:
I took the test and this was the correct answer
The function f(x) = 40(0.9)x represents the deer population in a forest x years after it was first studied. What was the deer population when it was first studied?
a. 44
b.40
c. 36
d.49
Answers
Answer:
36
Step-by-step explanation:
40*.9
Find the slope of a line perpendicular to a line through the given points. E(5, 7), F(3, 1)
Answers
Answer: -1/3
Step-by-step explanation:
The slope of the given line is [tex]\frac{7-1}{5-3}=\frac{6}{2}=3[/tex].
Thus, since perpendicular lines have slopes that are negative reciprocals of each other, the answer is -1/3
Lydia writes the equation below with a missing value.
y = 5 x minus box
She puts a value in the box and says that the equation represents a direct variation. Which explains whether the equation could represent a direct variation?
If she puts 0 in the box she would have a direct variation.
If she puts 5 in the box she would have a direct variation.
The equation is not of the form y = k x, so it cannot represent a direct variation.
The equation has a minus sign, so it cannot represent a direct variation.
Answers
If she puts 0 in the box she would have a direct variation.
Lydia writes the equation y = 5x - __ with a missing value.
She puts a value in the box and says that the equation represents a direct variation.
We have to choose the correct option from the given options that explain that the equation could represent a direct variation.
When two variables are such that one is a constant multiple of the other, we said they are in Direct variation.
What is the direct variation?
In form of y = ax, where y and x are in direct variation.
Consider the given equation y = 5x - __
For the equation to be in direct variation the value of the missing term has to be 0.
then the equation becomes,
y = 5x
Thus, If she puts 0 in the box she would have a direct variation.
Option (a) is correct.
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Answer:
a
Step-by-step explanation:
Design a real life activity for the Intermediate Phase in which learners will be required to apply the associative property of multiplication over addition.
Answers
The associative property of adding or multiplying can be represented by (a + b) + c = a + (b + c) and a * (b * c) = (a * b) * c
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The associative property states that when adding or multiplying it can be represented by:
(a + b) + c = a + (b + c)
For multiplication:
a * (b * c) = (a * b) * c
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Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-1, 2]? A. Both functions are increasing, but function f increases at a faster average rate. B. Only function f is increasing, but both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Only function f is increasing, and only function f is negative.
Answers
Both functions are increasing, but function g increases at a faster average rate.
The correct option is (C)
What is an increasing function?If the slope of a function is continuously increasing or constant in an interval, the function is known as an increasing function.
let f(x) = [tex]ab^{x} +c[/tex] and x=0 , f(0)= -10
-10=a+c
Now,
f(x) = -33/5*[tex](\frac{1}{11} )^{x}[/tex] - 17/5
f '(x)>0
So, x is increasing function.
g(x) = -18/3*[tex](\frac{1}{11} )^{x}[/tex] +2
g'(x) =-18[tex](\frac{1}{3} )^{x}[/tex]ln(1/3)
ln 1/3<0
So, g'(x)>0
So, g(x) is an increasing function.
For any x ∈ f(x) and x ∈ g(x)
Since, g increases at a faster rate.
Hence, Both functions are increasing, but function g increases at a faster.
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Step 2 of 2 : Suppose a sample of 782 suspected criminals is drawn. Of these people, 548 were not captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.
Answers
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.6625, 0.7388).
What is confidence interval?A confidence interval is the mean of your estimate plus and minus the variation in that estimate.
Given sample, n= 782
As, 548 were not captured.
x= 548
So, p= 548/ 782
p = 0.7007
q= 1- 0.7007 = 0.2993
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
Now,
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
For confidence level of 98% , z is 2.33
Now,
(0.70007 - 2.33√ (0.7007(0.2993))/782 , 0.70007 + 2.33 √(0.7007(0.2993))/782
= (0.6625, 0.7388)
Hence, 98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.6625, 0.7388).
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An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. The graph of this model would be:
a curved line that increases but then decreases.
a straight line that decreases only.
a straight line that increases only.
None of these choices are correct.
Answers
The graph of this model would be a straight line that increases only option third is correct.
What is a line graph?A line graph is a graph made up of segments of straight lines that connect the depicted data points.
We have:
An auto mechanic charges (C) an initial fee of $50 and then $40 per hour.
Let T be the total fee and h is the number of hours
T = 50 + 40h
The above equation represents a graph of a straight line as the slope of the line is positive.
m = 50
Thus, the graph of this model would be a straight line that increases only option third is correct.
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Given: a || b, transversal k
Prove <3 = <6
Answers
By the property of corresponding angles ∠3 ≅ ∠5.
What is transversal line?In geometry, a transversal is any line that intersects two straight lines at distinct points.
If two parallel lines are cut by a transversal, then each pair of corresponding angles are equals.
That is, ∠3 = ∠5 and ∠4 = ∠6.
Therefore the given angles ∠3 and ∠5 are equal.
Hence ∠3 ≅ ∠5 .
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8) 3/
of the magazines sold at a newsagents were wedding magazines.
What is this as a percentage?
44
Answers
Answer:
0.0085× 100= 0.85℅
Step-by-step explanation:
okay so you want 3/8 from 44 as percentage but how can you put the 3/8 on top of the 44 to multilply it by 100 to get the percentage, ofcourse we will have to change the 3/8 into a whole number. To do that we are going to do the following.
= 3 ÷ 8 = 0.375, so here you got a number that you can put on the 44.
Now to get the percentage we are going to do this:
0.375/44 × 100
= 0.0085 × 100 ( I solved the 0.375/44 as you know that division always comes first in maths)
= 0.85℅ ( I solved the 0.0085 × 100)
°•°•° I hope this helped sorry for taking long °•°•° May I get brainliest if you liked my ans im trying to lvl up ty and its okay if you don't want to
Mr. Garret has a total of 20 students in his class. The number of female students is 4 less than twice the number of male students. How many female and how many male students does he have?
Answers
Answer:
8 male, 12 female
Step-by-step explanation:
male = x
female = 2x - 4
2x - 4 + x = 20
3x - 4 = 20
3x = 24
x = 8
2(8) - 4 = 12
there are 8 male, 12 female
A rectangular fence has a perimeter of 184 feet. The length is four feet less than three times the width. Find the length and the width. = 2+2
Answers
Answer:
lenth = 68 [ft]; width=24 [ft].
Step-by-step explanation:
1) if the length is 'l' and the width - 'w', then it is possible
2) to write the condition 'The length is four feet less than three times the width' as 3w-4=l;
3) to write the given perimeter as 2(w+l)=184.
4) then it is possible to make up the system:
[tex]\left \{ {{2(w+l)=184} \atop {3w-4=l}} \right. \ = > \ \left \{ {{w+l=92} \atop {3w-l=4}} \right. \ = > \ \left \{ {{w=24} \atop {l=68}} \right.[/tex]
Help solve and get 20 pts! (Math)
Answers
The parent function of the quadratic function is x^2. Using this function for refrence, we see that there are some changed.
First, the function was shifted 2 units to the left, so we rewrite this as (x+2)^2, we also see that the function was also shifted 5 units up so we write, ((x+2)^2)+5, and finally, we see the function was flipped vertically, so we make this a negative,
(-(x+2)^2)+5.
Now, let's confirm this is the answer by plugging in the given coordinates!
5 = (-((-2)+2)^2)+5, ((0)^2)+5, 5.
1 = (-((-4)+2)^2)+5, ((-2)^2)+5, -4+5, 1.
please help me :((((((
Answers
Answer:
Answer D
Step-by-step explanation:
It says to divide f(x)/g(x), which is displayed in D and if we find the domain it would be x is not equal to -1/4
At the end of 2 years, P dollars invested at an interest rate r compounded annually increases to an amount, A dollars, given by the following formula. Upper A equals Upper P (1 plus r )squared Find the interest rate if $32 increased to $50 in 2 years. Write your answer as a percent.
Answers
The interest rate will be equal to 24% in 2 years.
What is compound interest?Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-
Given that:-
Find the interest rate if $32 increased to $50 in 2 years.The interest rate will be calculated by using the following formula:-
[tex]A = P[1+\dfrac{r}{n}]^{nt}[/tex]
[tex]50=32[1+\dfrac{r}{1}]^{2}[/tex]
[tex]\dfrac{50}{32}=(1+r)^2[/tex]
1.56 = ( 1 + r )²
√1.56 = ( 1 + r )
r = 1.24 - 1
r = 0.24
r = 24%
Therefore interest rate will be equal to 24% in 2 years.
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Which of the following staements must be true about this diagram check all that apply
Answers
Answer:Since, according to the Exterior Angle theorem, In a triangle the sum of any two adjacent interior angles is equal to the exterior angle of the triangle.
And, here is the exterior angle of the triangle, while , , and are the interior angles of the triangle.
Thus, according to the theorem,
.
⇒
and
Therefore, options B, C, E are correct.
Find two functions defined
implicity by this equation:
(x − 5)² − 3(y + 2)² = 4
Answers
Answer:
[tex] \frac{dy}{dy} = \frac{x - 5}{3y + 6} [/tex]
What is the equation of the line of symmetry for the parabola represented by the equation y=−2(x−7)2+11?
Enter your answer as the correct equation, like this: x = 42
Answers
Answer:
I think its x = 7
I belive it is
What are the values for y when x is 2, 4, and 6?
y = 20x + 7
Answers
When x is 4 y= 80+7 =87
When x is 6 y= 120+7 =127
four times a number is 48 less than 6 times the number
Answers
Answer:
the answer is 24
Step-by-step explanation:
6x - 48 = 4x
6x - 4x - 48 = 0
2x - 48 = 0
2x = 0 + 48
2x = 48
x = 24
44. What percent of Mary Brown's year-to-date
gross pay has been withheld for federal tax
purposes?
A. 10%
B 13%
C. 17%
D. 20%
45. For the pay period covered on this
paycheck, what percent of Mary Brown's
gross pay was withheld for all taxes and
voluntary dues?
A 10%
B. 13%
C 17%
D. 20%
Answers
Based on the amount of federal taxes withheld till date, the percent of Mary Brown's year-to-date that have been withheld is A. 10%.
The percent of the gross pay that has been withheld for all taxes and voluntary dues is C. 17%.
How much federal taxes have been withheld?= Fed tax till date / YTD Gross
= 662.26 / 6,318.17
= 10%
How much taxes and voluntary dues have been withheld?= (Fed tax + ST Tax + Med tax + Vol Due) / Current gross
= (111.42 + 17.09 + 12.25 + 2.5) / 845.10
= 17%
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let p be the perimeter of a rectangle, and let one side of the rectangle be x
PLEASE SHOW WORK
Answers
That is the length in terms of p and x.
L = p/2 - x
How to get the length of the other side in terms of x and p?
For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W).
Here we know that the perimeter is p, so P = p, and let's say that the width is x.
Then we can write:
p = 2*(L + x)
Solving for L:
L = p/2 - x
That is the length in terms of p and x.
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What is the value of x for the regular polygon shown below?
2x + 4
36
Answers
The table below shows the results of a screening program organized by Level 300 students of the department physiotherapy of the College Health Sciences of the University of Ghana. Complete the table and answer the questions below it using your understanding of probability and its applications to biomedical data.
True Diagnosis for presence of E. Coli
Test results Disease No Disease Total
Positive 35 15
Negative 10 60
Total
a. What is the efficiency of the test? 3 marks
b. What is the sensitivity of the screening kit? 3 marks
c. What is the specificity of the screening kit? 3 marks
d. What is the predictive value (PPV) of the test? 3 marks
e. What is the negative predictive value (NPV) of the test? 3 marks
(15 marks)
2. In double blinded randomized control trial for hypertensive patients attending Cocoa Clinic, thirty (30) 50-59-year-old were admitted into an intervention program for 6 weeks. During the trial, the average improvement in their systolic blood pressure was 15. The average improvement in systolic blood pressure in the general population of hypertensive patients is 20 with a standard deviation of 2.
i. What are the null and alternative hypotheses in this RCT? (2 marks)
ii. What tail is required in this test? (2 marks)
iii. What is the most appropriate statistical test for this study? (2 marks)
iv. State the assumptions of the test. (2 marks)
v. Test the above hypothesis using the appropriate statistical tool (7 marks)
Critical value =3.6
Answers
The ratio of the number of picture books encyclopedias, and fairy tale books Annette had is 3:4:5 She have half of her encyclopedias to her brother and he gave her 5 books of fairytales Now she has 14 more books of fairy tales than encyclopedias How many picture books does she have
Answers
The number of picture books does Annette have is 76 books.
Given the ratio of picture books , encyclopedias and fairy tales books is 3:4:5 and she have half of her encyclopedias to her brother and he gave her 5 books of fairytales
We need to find the number of picture books does she have
According to the statement the total number of books does Annette have is
3k+4k+5k = 12k
Where k is total number of books
Now , Picture book she have = 3/12k = 1/4k
Encyclopedia she have = 4/12k = 1/3k
Fairy tale she have = 5/12k
Here,
Encyclopedia +14 = Fairy tale
Substituting the values of Encyclopedia and Fairy tale
(1/3 -1/2)k +14 = (5/12k -5 )
Therefore.
(1/6k+14) = (5k/12-5)
Therefore,
14+5 = 5k/12 - k/6
Therefore,
19 = 3k/12
19*4=k
76 = k
Here k = 76 books
Hence the total number of picture books does she have is 76
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ADVANCED COSTING AND MANAGEMENT ACCOUNTING
A car engine manufacturer is trying to make an assessment of its operations for the past year. The
entity operates a standard marginal costing system and manufactures a state-of-the-art engine for
which the following standard revenue and cost data per unit of product is available:
Selling price $60.00
Direct material A 2.5 kg at $8.50 per kg
Direct material B 1.5 kg at $6.00 per kg
Direct labour 0.45 hrs. at $30.00 per hour
Actual data for the twelve-month period was as follows:
Sales and production 48,000 units of the blaster were produced and sold for $2,904,000
Direct material A 121,900 kg were used at a cost of $1,005,675
Direct material B 67,200 kg were used at a cost of $420,000
Direct labour Employees worked for 18,900 hours, but 19,200 hours were paid at a cost
of $585,600.
Budgeted sales for the period were 50,000 units of Product Blaster. A recession last year meant
that the market for the product declined by 5%.
Required:
(a) Calculate the following variances.
(i) Sales volume variance.
Answers
The Sales Volume Variance of the car manufacturer for the twelve-month period is $96,000.
What is the sales volume variance?The sales volume variance measures the financial impact of not meeting or exceeding the budgeted sales for a period.
It can be computed by finding the difference between actual and budgeted sales quantities and then multiplied by the unit selling price.
Data and Calculations:Budgeted sales units = 50,000
Actual sales units = 48,000
Sales price per unit = $60
Actual sales revenue = $2,904,000
Budgeted sales revenue = $3,000,000 ($60 x 50,000)
Sales volume variance = $96,000 ($3,000,000 - $2,904,000)
Thus, the Sales Volume Variance is $96,000.
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Two buses leave a station at the same time and travel in opposite directions. One bus travels 14 miles faster than the other. If the two buses are 640 miles apart after 5 hours, what is the rate of each bus?
Answers
If the two buses are 640 miles apart after 5 hours. Then the rate of each bus will be 57 miles per hour and 71 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Two buses leave a station at the same time and travel in opposite directions.
One bus travels 14 miles faster than the other.
Let x be the speed of first bus. Then the speed of the second bus will be (x + 14).
If the two buses are 640 miles apart after 5 hours.
Then the rate of each bus will be
Then the relative speed of the buses will be
S = x + x + 14
S = 2x + 14
Then the value of x will be
2x + 14 = 640 / 5
2x + 14 = 128
2x = 114
x = 57 miles per hour
Then the speed of the other bus will be
⇒ 57 + 14
⇒ 71 miles per hour
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Prove that < AOD and < BOD are supplementary
Answers
Angle AOD and < BOD are supplementary since they are both right angles which equal 180°.
What is a supplementary angle?It should be noted that a supplementary angle simply means an angle that adds up to 180°.
In this case, the angles given are both rights angles. This will be:
= 90° + 90°
= 180°
In this case, Angle AOD and < BOD are supplementary since they are both rights angles which equal 180°.
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