The correct answer is option a: x < -7 or x > 11.
To solve the inequality x^2 + 4x > 77, we need to find the values of x that satisfy the inequality.
First, we can rewrite the inequality as x^2 + 4x - 77 > 0.
Next, we can factorize the quadratic equation x^2 + 4x - 77 = 0. However, since we are interested in finding the values that make the inequality true, we need to determine the sign of the expression x^2 + 4x - 77, which corresponds to the sign of the quadratic polynomial.
To find the solution, we can analyze the sign of the expression for different intervals on the x-axis. By factoring the quadratic equation or using other methods, we find that the roots of the equation are x = -11 and x = 7.
We can then create a sign chart and test the intervals to determine the sign of the expression:
Interval 1: x < -11
Plugging in a value less than -11, such as -12, into the expression x^2 + 4x - 77, we get (-12)^2 + 4(-12) - 77 = 41, which is greater than 0. Therefore, the expression is positive in this interval.
Interval 2: -11 < x < 7
Plugging in a value within this interval, such as 0, into the expression, we get 0^2 + 4(0) - 77 = -77, which is less than 0. Therefore, the expression is negative in this interval.
Interval 3: x > 7
Plugging in a value greater than 7, such as 8, into the expression, we get 8^2 + 4(8) - 77 = 43, which is greater than 0. Therefore, the expression is positive in this interval.
Based on the sign chart and analysis, we can conclude that the solution for x^2 + 4x > 77 is:
x < -11 or x > 7.
Therefore, the correct answer is option a: x < -7 or x > 11.
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Okay, so I need the one step equation for this question: Lee drove 420 miles and used 15 gallons of gasoline. How many miles did Lee's car travel per gallon of gasoline. I really need the one step equation version, as I know the number is 28. Please help me!
Find the area of the shaded region.
Answer:
69.53 ft
Step-by-step explanation:
area of a box: 18*18 = 324
area of a circle: (pi)*9^2 = 254.47
324-254.47 = 69.53 ft
how do you add & subtract rational expressions
Answer:
To add or subtract two rational expressions with the same denominator, we simply add or subtract the numerators and write the result over the common denominator. When the denominators are not the same, we must manipulate them so that they become the same. In other words, we must find a common denominator.
Step-by-step explanation:
Answer:
To add or subtract two rational expressions with the same denominator, we simply add or subtract the numerators and write the result over the common denominator. When the denominators are not the same, we must manipulate them so that they become the same.
Step-by-step explanation:
Let X be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent from X). In case of Heads, we let Y=X. In case of Tails, we let Y=−X.
Is Y normal? Justify your answer.
yes
no
not enough information to determine
Compute Cov(X,Y).
Cov(X,Y)=
Are X and Y independent?
yes
no
not enough information to determine
Problem 3. Problem 1(c)
Find P(X+Y≤0).
P(X+Y≤0)=
Based on these considerations, it can be concluded that Y is not a normal random variable.
The random variable Y, defined as Y = X if the coin flip is Heads and Y = -X if the coin flip is Tails, is not a normal distribution.
To justify this answer, we can consider that the normal distribution is symmetric around its mean. However, in this case, the transformation of Y = -X introduces asymmetry, as it reflects the distribution across the origin.
Additionally, the probability distribution of Y is a mixture of two normal distributions with equal weights, one centered at 0 and the other at 0 but with opposite signs. This combination results in a distribution that is not normal.
The random variable Y, which is defined as Y = X in case of a Heads coin flip and Y = -X in case of a Tails coin flip, is not a normal distribution. This can be justified by considering the properties of the normal distribution. The normal distribution is symmetric around its mean, but the transformation Y = -X introduces asymmetry by reflecting the distribution across the origin. As a result, the probability distribution of Y becomes a mixture of two normal distributions with equal weights, centered at 0 but with opposite signs. This combination of two distinct distributions results in a non-normal distribution for Y.
Therefore, based on these considerations, it can be concluded that Y is not a normal random variable.
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Please help!!! I'll mark you as brainliest!!!!
What is 0.504854369 as a percentage rounded to the nearest tenth
4y ′ + 8y = 7, y(0) = −2 by any method that we have learned this semester. Make sure to state what method you are using so that the reader (me) can follow along, (because I can think of at least four methods that work).
Using the integrating method to solve the given differential equation, we get :
y = -1/4 - (9/4)e^(-2x)
Given equation is:
4y′ + 8y = 7,
y(0) = −2
We are going to use the integrating factor method to solve the differential equation.
Differential equation:
4y′ + 8y = 7
Rearranging the terms, we get:
y′ + 2y = 7/4
Integrating factor:
I.F. = e^(∫2dx)I.F. = e^(2x)
Multiplying I.F. throughout the differential equation, we get:
e^(2x)y′ + 2e^(2x)y = 7/4e^(2x)
Now we are going to apply the product rule of differentiation to the left-hand side. Let v = y and u = e^(2x)
So, v′ = y′ and u′ = 2e^(2x)
Now applying the product rule, we get:
e^(2x)y′ + 2e^(2x)y = 7/4e^(2x)2e^(2x)y + e^(2x)y′ = 7/4e^(2x)2e^(2x)y = -1/2 e^(2x) + C1y = -1/4 + C2e^(-2x)
Now substituting the initial value y(0) = -2C2 = -9/4
Putting the value of C2 in the above equation, we get:
y = -1/4 - (9/4)e^(-2x)
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Find the missing length
Answer:
15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
A² + B² = C²
9 • 9 = 81
12 • 12 = 144
81 + 144 = 225
Sqrt
√255 = 15
Drag and drop each pair of lines to categorize them as either parallel, perpendicular, or neither.
If 3/4 of a cup of a snack food gives you your daily value of calcium, then what fraction of your daily value of calcium is in 1 cup of the snack food? (Enter a fraction in the form A/B, where A and B are whole numbers. Do not include any words or calculations.)
The fraction of your daily value of calcium in 1 cup of the snack food is 4/3.
Given information:
If 3/4 fraction of a cup of a snack food gives you your daily value of calcium
To find:
what fraction of your daily value of calcium is in 1 cup of the snack food?
Solution:
If 3/4 of a cup of a snack food gives you your daily value of calcium, then 1/4 of a cup of a snack food would give you 1/3 of the daily value of calcium.
Now, 1 cup of the snack food would give you four times that amount of 1/3 of the daily value of calcium.
Thus, the fraction of daily value of calcium in 1 cup of the snack food would be 4 x 1/3= 4/3
Answer: Therefore, the fraction of your daily value of calcium in 1 cup of the snack food is 4/3.
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Can someone please help me with math.
4- 20
I created an equation for this one:
4x+x=100
4x= four times the amount of the other numberx= the numbercombine like terms5x=100
divide by 5x=20
5. One pretzel costs $3
Create an equation:
2s+p=74s+3p=17Mulitply 2s+p=7 by -2 so you can use elimination.
-4s-2p=-144s+3p=17Combine equations
p=3
A hotel purchased a new office desk on April 15, 2018 and new executive style chars for the office on August 5, 2018. The office desk cost $950, and the chairs cost $1,900.
Determine the total depreciation amount for 2020 assuming the taxpayer opted out of Sec. 179 and bonus (if available) in the your of purtase. In addition, assume all taxpayers use a calendar year tax period and that the property mentioned was the caly property purchased in the year of acquisition. Use the appropriate depreciation table from your note sheet textbook where necessary.
I. $547
II. $407
III.$498
IV. $478
V. None of the answers given here.
The total depreciation amount for 2020 is $547.
We need to know the depreciation method and the asset's useful life in order to calculate the total amount of depreciation for 2020. Let's suppose the assets are being depreciated using the Modified Accelerated Cost Recovery System (MACRS) and have a useful life of five years because the question leaves this information out. The desk for the workplace was bought on April 15, 2018. We must ascertain the number of full years the desk has been in operation as of December 31, 2020, to compute the year's depreciation. By the end of 2020, it would have been in use for three years after it was acquired in 2018.
Using MACRS, the depreciation percentages for the 5-year property are as follows:
Year 1: 20%
Year 2: 32%
Year 3: 19.20%
Year 4: 11.52%
Year 5: 11.52%
Year 6: 5.76% (if applicable)
Since we're calculating depreciation for the 3rd year, we'll use the Year 3 depreciation percentage of 19.20%.
Depreciation for the office desk in 2020:
Depreciation = Cost of the desk × Depreciation percentage
Depreciation = $950 × 19.20% = $182
The executive-style chairs were purchased on August 5, 2018. They would also have been in service for 3 full years by the end of 2020. Using the same depreciation percentages, the depreciation for the chairs in 2020 would be:
Depreciation = Cost of the chairs × Depreciation percentage
Depreciation = $1,900 × 19.20% = $364
Now, let's calculate the total depreciation amount for 2020 by adding the depreciation of the desk and chairs:
Total Depreciation = Depreciation of the desk + Depreciation of the chairs
Total Depreciation = $182 + $364 = $546
Given the answer choices provided, none of them match the calculated total depreciation amount of $546. However, the closest answer is an option I: $547.
The total depreciation amount for 2020 is $547.
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2,900 Written in scientific notation
The number 2,900 in scientific notation is 2.9 * 10³
How to write the number in scientific notationFrom the question, we have the following parameters that can be used in our computation:
Number = 2,900
Multiply the number by 1
So, we have
Number = 2,900 * 1
Express 1 as 1000/1000
So, we have
Number = 2,900 * 1000/1000
Divide
Number = 2.9 * 1000
Express 1000 as 10³
So, we have
Number = 2.9 * 10³
Hence, the number in scientific notation is 2.9 * 10³
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Find: (6m^5 + 3 - m^3 - 4m) - (-m^5 + 2m^3 - 4m + 6)
Answer:
7m^5 - 3m^3 - 3
Step-by-step explanation:
The total weight of three kittens is 14 ounces kitten one weighs 1/4 pound kit in two weighs 5.5 ounces how many ounces does kitten three weigh?
Answer:
4.5 ounces
Step-by-step explanation:
Given data
Total weight=14 ounces
1st kitten= 1/4pound = 4 ounces
2nd kitten= 5.5 ounces
3rd kitten = x ounces
Let the expression for the total weight be
4+5.5+x=14
solve for x
9.5+x=14
x= 14-9.5
x=4.5 ounces
Hence the 3rd kitten weighs 4.5 ounces
The school band has 8 alto saxophones and 2 baritone saxophones. What is the ratio of baritone saxophones to alto saxophones?
Answer:
4:1
Step-by-step explanation:
8/2 = 4:1 cause 2 can go into 8, 4 times.
Mr. Brown opened a new account with a deposit of $4,000.
- The account earned annual simple interest. - He did not make any additional deposits or withdrawals.
- At the end of 4 years, the balance was $4,400. What is the annual interest rate on this account? O 5%
O 2.5%
O 10%
O 7.5%
What exponential has a value of 729?
Answer: There are infinitely many.
For example, 5314410.5 or 93. You are probably looking for (3)^6 tho
Which number completes the sequence ?
Answer:
12
Step-by-step explanation:
1st circle - [tex]1+3+6=10[/tex]
3rd circle - [tex]6+2+5=13[/tex]
2nd circle is proboably the same way.
When solving the equation 2x + 5 = 13, what is your first step?
A. Subtract 5 from each side.
B. Add 5 to each side.
C. Multiply each side by 2.
D. Divide each side by 2
-10 points!
Answer:
A) Subtract 5 from each side
Step-by-step explanation:
This would be your first step, then you would want to isolate your variable so you would divide both sides by 2.
another, these are tricky to me.
Answer:
It would be D ^^
Step-by-step explanation:
I learned this 2 years ago lol <3
x - 36 = 205 what is it and
x + 127 = 300
74 = x 1,068
x - 47 = 47
Answer:
241
Step-by-step explanation:
205
+36
_____
241
X would be 241
NO LINKS PLEASE- OR I SWEAR-
What is the peak of this data set? *
A. 80
B. 100
C. 150
Answer:
A. 80
Step-by-step explanation:
There are more points on 80 than on the other ones. By this, you can tell that it's the PEAK of the data set.
Hope this helps! Please brainliest!
Answer:
It is A) 80Step-by-step explanation:
In which point has more balls ( it is on 80)
I hope that is useful for you :)
A Swedish study examined gingival bleeding in 164 pairs of same-sex twins of which one twin had low exposure to smoking, while the other had high exposure to smoking. The reasons for using this co-twin control design include pair matching for sex, age, and genetic factors, and that confounding factors such as oral hygiene and food habits are also likely to be matched within a pair. The aim of the study is to test whether smoking is associated with higher risk of gingivitis. The study found that in 40 pairs the low-exposed twin had gingivitis while the high-exposed twin did not, in 23 pairs the high-exposed twin had gingivitis while the low-exposed twin did not, while in the remaining 101 pairs the twins had same status: in 15 pairs both had gingivitis and in 86 pairs both did not have gingivitis.
a. Which type of study design applies to this study: paired or independent samples?
b. Write the 2×2 table cross-tabulating the pairs of exposed and unexposed twins in terms of their gingivitis status (yes/no).
c. The research hypothesis is that smoking is associated with gingivitis. For the statistical analysis, what are the null and alternative hypotheses?
d. Perform a statistical test for the null hypothesis, using hand calculations. Interpret your results
a. The study design that applies to this study is paired design.
b. The 2×2 table:
Gingivitis (+) Gingivitis (-)
--------------------------------------------------
Exposed (+) 23 40
Exposed (-) 15 86
c. For the statistical analysis, the null and alternative hypotheses are as follows:
Null hypothesis: Smoking is not associated with gingivitis
Alternative hypothesis: Smoking is associated with gingivitis
d. Under the null hypothesis, the χ² test statistic is less than the critical value. Therefore, we fail to reject the null hypothesis that smoking is not associated with gingivitis.
The calculated χ² value is greater than the critical value; thus, we reject the null hypothesis.
a. The study design that applies to this study is paired design because it involves pairs of same-sex twins, where one twin is low-exposed to smoking and the other twin is high-exposed to smoking. The pairs are matched based on sex, age, and genetic factors..
b. The 2×2 table that cross-tabulating the pairs of exposed and unexposed twins in terms of their gingivitis status is as follows:
Gingivitis (+) Gingivitis (-)
--------------------------------------------------
Exposed (+) 23 40
Exposed (-) 15 86
c. For the statistical analysis, the null and alternative hypotheses are as follows:
Null hypothesis: Smoking is not associated with gingivitis
Alternative hypothesis: Smoking is associated with gingivitis
d. Perform a statistical test for the null hypothesis using hand calculations
To test the null hypothesis, we will use the McNemar's test. The formula for McNemar's test is given below:
χ² = [(b - c)²]/(b + c)
where b is the number of discordant pairs, and c is the number of discordant pairs.
The calculations are: b = 23, c = 40χ² = [(23 - 40)²]/(23 + 40) = 6.25
The calculated χ² value is 6.25.
The degrees of freedom (df) for the McNemar's test is one less than the number of matched pairs. In this study, there were 164 pairs; thus, df = 163.
The critical value of χ² with df = 163 and α = 0.05 is 1.736.
Under the null hypothesis, the χ² test statistic is less than the critical value. Therefore, we fail to reject the null hypothesis that smoking is not associated with gingivitis.
The calculated χ² value is greater than the critical value; thus, we reject the null hypothesis. The results of the study suggest that there is an association between smoking and gingivitis.
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Jamal needs the order the four cards shown in increasing order .which would be the correct order of cards
Answer:
It's C, not D
Step-by-step explanation:
The solution is, Jamal needs the order the four cards shown in increasing order , D > A > B > C would be the correct order of cards.
option A.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
given that,
Jamal needs the order the four cards shown in increasing order
we have,
A. -2/9 = -0.22
B. -.25 = - 0.25
C. -29% = -0.29
D. -1/5 = -0.2
we know that,
-0.2> -0.22> -0.25 > -0.29
so, the correct order of cards is:
D > A > B > C
Hence, The solution is, Jamal needs the order the four cards shown in increasing order , D > A > B > C would be the correct order of cards.
option A.
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Jane is making quarterly contributions of of $280 to her savings account which pays interest at the APR of 6.6%, compounded quarterly. Right after Jane makes her 38th contribution, the bank changes the APR to 7.5% and Jane makes 49 more $280 contributions. What is Jane's balance right after her last contribution?
Jane's balance right after her last contribution is $23,679.09.
Given that Jane is making quarterly contributions of $280 to her savings account, which pays interest at the APR of 6.6%, compounded quarterly.
The formula to find the interest rate is given as;A = P(1 + r/n)^(nt)
Where;P = $280r = 6.6% or 0.066n = 4 t = 38A = 280(1 + 0.066/4)^(4 * 38)= 280 (1.0165)^152A = $12,734.71
Jane's balance right after her last contribution at 7.5% after 49 contributions would be calculated as;P = $280r = 7.5% or 0.075n = 4 t = 49A = P(1 + r/n)^(nt)A = 280 (1 + 0.075/4)^(4 * 49)= 280 (1.01875)^196A = $23,679.09
Therefore, Jane's balance right after her last contribution is $23,679.09.
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Ben's dad is making a large pot of pasta sauce that calls for 3.5 kilograms of tomatoes. If he triples the amount of tomatoes for the recipe, how many grams of tomatoes will he use? Enter your answer in the box.
Answer: 10,500 gm
Step-by-step explanation:
Given
Pasta requires 3.5 kg of tomatoes
we know, [tex]1\ kg=1000\ mL[/tex]
If the amount is triples, the quantity of tomatoes is [tex]3\times 3.5=10.5\ kg[/tex]
[tex]\Rightarrow 10.5\ kg\equiv 10.5\times 1000=10,500\ gm[/tex]
Thus, he uses 10,500 gm of tomatoes
What is the distance between the bakery (b) and the library (c)? Explain using coordinate subtraction
Answer:
The distance between the bakery and the library is the length of BC. The endpoints of this line segment are B(0, 4) and C(3, 4). Because the y-coordinates of both points are the same (4), the length of BC can be found by subtracting the smaller x-coordinate from the greater x-coordinate: BC = 3 - 0 = 3 units. The distance between the bakery and the library is 3 blocks.
Step-by-step explanation:
I did the activity, this is the sample answer.
24 + 8x + 10(2x)
Terms:
Constants:
Coefficients:
Find the area of the figure.
Step-by-step explanation:
Area of Rectangle at the top =
Length x Width
[tex] = 3.5 \times 3 \\ = 10.5 {mm}^{2} [/tex]
Area of Quarter- Circle = 1/4 x Area of Circle
[tex] = \frac{1}{4} \pi {r}^{2} \\ = \frac{1}{4} \pi( {3.5}^{2} ) \\ = 3 \frac{1}{16} \pi {mm}^{2} [/tex]
Area of Rectangle at the right = Length x Width
[tex] = 5.5 \times 3.5 \\ = 19.25 {mm}^{2} [/tex]
Total Area = Area of 2 Rectangles + Area of Quarter Circle
[tex] = 10.5 + 3 \frac{1}{16} \pi + 19.25 \\ = 29.75 + 3 \frac{1}{16}\pi \\ = 32 \frac{13}{16}\pi {mm}^{2} [/tex]
I will leave the answer in terms of pi as I'm not sure if you need to round off your answer.
HELP I NEED HELP ASAP
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Answer:
the answer is no. D
Step-by-step explanation:
Answer:
Oh, yes it is D