Answer:
Th correct option is (d).
Step-by-step explanation:
The given expression is :
[tex]16x^2 + nx + 49[/tex] ....(1)
We know that, 16 = 4² and 49 = 7²
Also, (a+b)² = a²+2ab+b²
The given expression becomes,
[tex]16x^2 + nx + 49=(4x)^2+nx+7^2\\\\=(4x)^2+2(4x)(7)+7^2\\\\=16x^2+56x+49\ ......(2)[/tex]
Comparing equations (1) and (2),
n = 56
Hence, the value of n is equal to 56.
An airplane travels 240 miles in 3 hours with the wind. The return trip against the wind takes 4 hours. What is the wind speed and the speed of the airplane in still air?
Answer:
Let p = the speed of the plane
and w = the speed of the wind
It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. So we set up a system of equations.
600mi3hr=p−w600mi2hr=p+w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation. I'll solve for x in the first equation:
200mph = p - w
Add w to both sides:
p = 200mph + w
Now we can substitute the x that we found in the first equation into the second equation so we can solve for w:
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
Divide by 2:
50mph = w
So the speed of the wind is 50mph.
Now plug the value we just found back in to either equation to find the speed of the plane, I'll plug it into the first equation:
200mph = p - 50mph
Add 50mph on both sides:
250mph = p
So the speed of the plane in still air is 250mph.
Answer:
140miles/hour
Step-by-step explanation:
Speed of airplane + speed of wind
=240miles/3 hours + 240miles/4 hours
=80miles/hour +60miles/hour
= 140miles/hour
9×3 n =3 powered by 7 slove n
Answer:
81
Step-by-step explanation:
9 × 3n= 3^7
9×3n= 2187
27n= 2187
n= 2187/27
= 81
Hence n= 81
Solve: x^2 – 16x + 63 < 0
Answer:
7 < x < 9
Step-by-step explanation:
x^2 – 16x + 63 < 0
this is a parabola that opens up.
The parabola will be < 0 for values between the roots.
to picture this see the graph below.
Factor
(x - 7)(x - 9) < 0
Roots
x = {7, 9}
solution
7 < x < 9
A sample of college freshmen was asked how many hours per week they spent playing video games. The following frequency distribution presents the results. Number of Hours Frequency - - - - - - - - - - Part 1 of 2 (a) How many classes are there
Answer:
Step-by-step explanation:
Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.
Similarities and Differences in a Random Sample of 375 Married Couples
Number of Similar Preferences Number of Married Couples
 All four                     29
Three                     124
Two                     120
One                     66
None                     36  Â
Suppose that a married couple is selected at random.
Required:
Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common.
Answer:
P ( All four) = 29/375=0.07733
P ( Three A^) = 124/375= 0.33067
P ( Two A^) = 120/375= 0.32
P (One A^) = 66/375= 0.176
P (None A^) = 36/375= 0.096
Step-by-step explanation:
Number of Similar Preferences  Number of Married Couples
All four 29
Three 124
Two 120
One 66
None 36
Total 375
We want to determine the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common.
P ( All four) = 29/375=0.07733
P ( Three A^) = 124/375= 0.33067
P ( Two A^) = 120/375= 0.32
P (One A^) = 66/375= 0.176
P (None A^) = 36/375= 0.096
Probability is calculated by favorable outcome divided by the total outcome.
Similarly we obtained the probabilities of the couples that they will have 0, 1, 2, 3, or 4 personality preferences in common.
Evaluate: 7( 14 - 8) - 6²
5
6
7
8
please help if possible 3
Answer:
6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
7(14 - 8) - 6²
Step 2: Evaluate
Exponents: 7(14 - 8) - 36(Parenthesis) Subtract: 7(6) - 36Multiply: 42 - 36Subtract: 6Whats 5x=234 please answer i will brainliest if i can
Answer:
x = 46.8
Step-by-step explanation:
I assume you are trying to find the value of x.
[tex]5x=234.[/tex]
To find x, divide the answer by the coefficient. The quotient is the value of 'x.'
[tex]234/5=46.8[/tex]
Therefore, 46.8 is the value of x.
Remember: Whenever you see a coefficient and a variable together—5x, 7y, 3t—this means to multiply them.
Cora's dad has asked Cora and her little brothers to rake the leaves in their yard. They rake all afternoon and fill a number of bags with leaves. Then, when Cora isn't looking, her brothers empty 6 of the bags to make a giant leaf pile! Cora is frustrated that only 5 bags of leaves remain. What equation can you use to find the total number of bags b that Cora and her brothers fill with leaves?
Answer:
11
Step-by-step explanation:
because they empty 6 bags and there are 5 bags left to that is 11 all together
The total number of bags of leaves b is given by the equation b = 11 bags
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the total number of bags be = b
The number of bags emptied by Cora's brother = 6 bags
The number of bags left with Cora = 5 bags
So , the equation will be
The total number of bags b = number of bags emptied by Cora's brother + number of bags left with Cora
Substituting the values in the equation , we get
The total number of bags b = 6 + 5
The total number of bags b = 11 bags
Therefore , the value of A is 11 bags
Hence , the number of bags of leaves is 11 bags
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
At-home medical test kits have increased in popularity in recent years. This year, 380 million test kits are expected to be sold. This represents a 114% increase from the number of kits that were sold last year. How many medical test kits were sold last year?
Answer:
326.8 million
Step-by-step explanation:
You just get 14% of 380 million and subtract it from 380 million
Find the value of given PSRQ is a parallelogram
Angle S and angle R are supplementary angles and need to add together to equal 180 degrees.
This means angle r = 180-145 = 35 degrees.
36x -1 = 35
Add 1 to both sides:
36x = 36
Divide both sides by 36
X = 1
Answer:
Work attached below :D
A brand new car was purchased for $28,000 in year 2000. The car value has dropped to
$20,000 in year 2003. What could be considered as the rate of depreciation?
(Round your answers to the nearest 10th.)
Answer:
The rate of depreciation is 11.87% per year.
Step-by-step explanation:
Given that a brand new car was purchased for $ 28,000 in year 2000, and the car value has dropped to $ 20,000 in year 2003, to determine what could be considered as the rate of depreciation, the following calculation must be performed:
20,000 x (1 + X / 1) ^ 3 = 28,000
20,000 x X ^ 3 = 28,000
20,000X ^ 3 = 28,000
X = 1.1187
Therefore, the rate of depreciation is 11.87% per year.
Choose all of the following relationships that represent functions
I need help I have been stuck on this for years. Plz anything helps
9514 1404 393
Answer:
see below
Step-by-step explanation:
Perhaps you're stuck because it is too simple. If any value in the x-column is repeated, the relation is not a function.
Of the two relations shown, the first is not a function (x=3 is repeated), and the second one is a function (all the x-values are different).
What the answer? quickly please?
Answer:
the 1st choice
Step-by-step explanation:
MARK BRAINLIEST
help with this please. Thanks
9514 1404 393
Answer:
3.0
Step-by-step explanation:
The angle, its opposite side, and the hypotenuse are given. Then the relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(21°) = x/8.3 . . . . . . . . . . . . . . . . . . use the given values
x = 8.3·sin(21°) ≈ 8.3×0.3584 . . . . . . multiply by 8.3
x ≈ 3.0
If f (x) is an exponential function where f(-2.5) = 9 and f(7) = 91, then find
the value of f(12), to the nearest hundredth.
Cardiovascular disease is a major cause of death and illness worldwide, with high blood pressure and high LDL cholesterol both being established risk factors. Because most cardiovascular events occur in persons with average risk factors. Because most cardiovascular events occur in persons with average risk and no previous cardiovascular disease history, the present research examined the simultaneous use of both blood pressure reducing drugs and cholesterol reducing drugs on this population, rather than focusing on only those on only those at high risk. Subjects included men at least 5 years old and women at least 6565 years old without cardiovascular disease who had at least one additional risk factor besides age, such as recent or current smoking, hypertension, or family history of premature coronary heart disease. Those with current cardiovascular disease were excluded from the study. Subjects were randomly assigned to the treatment (cholesterol and blood pressure reducing drugs) or a placebo, and the number suffering the primary outcome of a fatal cardiovascular event, a nonfatal myocardial infarction or a nonfatal stroke, were observed. Provided are the results for the two groups over the course of the study:
Group Sample size Number experiencing primary outcome
Treatment 3180 113
Placebo 3168 157
Let p1 be the proportion experiencing the primary outcome with the treatment and p2 the proportion without the treatment. Select the correct pair of hypotheses.
a. H0:p1=p2 versus Ha:p1â p2 .
b. H0:p1=p2 versus Ha:p1>p2 .
c. H0:p1=p2 versus Ha:p1
d. None of the options are correct.
Answer:
H0: p1=p2 versus Ha:p1≠p2
Step-by-step explanation:
Let p1 be the proportion experiencing the primary outcome with the treatment and p2 the proportion without the treatment.
We want to determine whether the proportion of persons having the treatment suffering the primary outcome of a fatal cardiovascular event is equal to the proportion of people without the treatment suffering the primary outcome of a fatal cardiovascular event.
The hypothesis is based on the study under observation. The claim is set as the alternate hypothesis.
The null and alternate hypotheses are
H0: p1=p2 versus Ha:p1≠p2
Both proportion ( with and without treatment ) are same
against the claim
Both proportion ( with and without treatment ) are not the same .
Option which gives the answer
H0: p1=p2 versus Ha:p1≠p2
is the best option.
Two planes, which are 3740 miles apart, fly towards eah other. Their speeds diifer by 35 miles per hour. If they pass eah other in 4 hours what is the speed of each.
Answer:
In 4 hours they flew a combined 3740/4 = 935mph or 467.5mph each. +/- 17.5 to this number,
485mph & 450mph are their speeds.
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
pls help oooooooooooooopoo
9514 1404 393
Answer:
140°
Step-by-step explanation:
Angles 1 and 3 are "corresponding" angles, so are congruent.
∠1 = ∠3
20x +60 = 30x +20
40 = 10x . . . . . . . . . . . . subtract 20x+20
4 = x . . . . . . . . . . . . . . divide by 10
∠1 = 20x +60 = 20(4) +60 = 80 +60
∠1 = 140°
Answer:
140°
Step-by-step explanation:
Angle 1 and angle 3 are corresponding angles ;
Corresponding angles are equal ;
Hence,
Angle 1 = Angle 3
20x + 60 = 30x + 20
Collect like terms
20x - 30x = 20 - 60
-10x = - 40
x = 4
Angle 1 is thus :
20x + 60 ; x = 4
20(4) + 60
80 + 60
= 140°
Please help me I beg you, I don’t understand and no one wants to help
Answers:
x = 51
y = 39
===========================================================
Explanation:
The angles 39 and x form a right angle, aka 90 degree angle. This is shown by the small square angle marker.
One equation to solve is x+39 = 90. Doing so leads to x = 51 after subtracting 39 from both sides.
Similarly, another equation to solve is x+y = 90. Plug in x = 51 and isolate y
x+y = 90
51+y = 90
y = 90-51
y = 39
Question 2
Suppose you put $5,000 in a savings account with an annual interest rate of 3%
compounded monthly for three years. What is the future value of this investment?
$5,280
$5,440
$5,470
$5,415
Answer:
5470
Step-by-step explanation:
[tex]5000(1+\frac{.03}{12})^{12*3}=5470.257[/tex]
The future value of the investment in the savings account with montly compounding is $5470.
What is the future value?When an investment is compouded monthly, it means that it increases in value every month.
The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate = 3%/12 m = number of compounding = 12 N = number of years5000 x ( 1.0025)^36 = $5470
To learn more about future value, please check: https://brainly.com/question/18760477
Which statement is true?
Question 16 options:
A)
–|–45| = 45 and –|–96| = –96.
B)
|–45| = –45 and |–96| = –96.
C)
|–45| = 45 and |–96| = 96.
D)
|–45| = 45 and |–96| = –96
Answer:
I think D is the answer
Can you please give me Brainliest answer plz
Answer:
C is the correct answer.
Help... do I add or divide?
he owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on weekdays and weekends. The owner samples 5 weekdays and finds an average of 259.23 gallons of milk sold on those days with a standard deviation of 34.713. 10 (total) Saturdays and Sundays are sampled and the average number of gallons sold is 365.12 with a standard deviation of 48.297. Construct a 90% confidence interval to estimate the difference of (average number of gallons sold on weekdays - average number of gallons sold on weekends). Assume the population standard deviations are the same for both weekdays and weekends.
Answer:
90% confidence interval is ( -149.114, -62.666 )
Step-by-step explanation:
Given the data in the question;
Sample 1 Sample 2
x"₁ = 259.23 x"₂ = 365.12
s₁ = 34.713 s₂ = 48.297
n₁ = 5 n₂ = 10
With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }
significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1
Since we are to assume that variance are equal and they are know, we will use pooled variance;
Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13
Now, pooled estimate of variance will be;
[tex]S_p^2[/tex] = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]
we substitute
[tex]S_p^2[/tex] = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]
[tex]S_p^2[/tex] = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [ 4 + 9 ]
[tex]S_p^2[/tex] = [ 4819.9692 + 20993.4 ] / [ 13 ]
[tex]S_p^2[/tex] = 25813.3692 / 13
[tex]S_p^2[/tex] = 1985.64378
Now the Standard Error will be;
[tex]S_{x1-x2[/tex] = √[ ( [tex]S_p^2[/tex] / n₁ ) + ( [tex]S_p^2[/tex] / n₂ ) ]
we substitute
[tex]S_{x1-x2[/tex] = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]
[tex]S_{x1-x2[/tex] = √[ 397.128756 + 198.564378 ]
[tex]S_{x1-x2[/tex] = √595.693134
[tex]S_{x1-x2[/tex] = 24.4068
Critical Value = [tex]t_{\frac{\alpha }{2}, df[/tex] = [tex]t_{0.05, df=13[/tex] = 1.771 { t-table }
So,
Margin of Error E = [tex]t_{\frac{\alpha }{2}, df[/tex] × [ ( [tex]S_p^2[/tex] / n₁ ) + ( [tex]S_p^2[/tex] / n₂ ) ]
we substitute
Margin of Error E = 1.771 × 24.4068
Margin of Error E = 43.224
Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89
So, Limits of 90% CI will be; x₁ - x₂ ± E
Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114
Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666
Therefore, 90% confidence interval is ( -149.114, -62.666 )
If a seed is planted, it has a 75% chance of growing into a healthy plant.
If 6 seeds are planted, what is the probability that exactly 4 don't grow?
Answer:
It is binomial:
p= 0.75 = 75%
1-p = 0.25 = 25%
N = 10
k=7
"seven successes in 10 trials"
(10 choose 7) (0.75)^7 ( 0.25)^3 =
(10*9*8 / 3*2) * (0.75)^7 ( 0.25)^3 =
(5*3*8) (0.75)^7 ( 0.25)^3
120 (0.75)^7 ( 0.25)^3
= 0.25028228759765625
or just over 25%
Step-by-step explanation:
how do you solve the formula for an unknown variable in terms of the known variables? For context, the question deals with principal investments.
0.088 is more than 0.78, right?
Hi there!
»»————- ★ ————-««
I believe your answer is:
No.
[tex]0.088 < 0.78[/tex]
»»————- ★ ————-««
Here’s why:
0.088 can be described as "eighty-eight thousandths". 0.78 can be described as "seventy-eight hundredths."Thousandths has a lesser value than hundredths. 0.088 is less than 0.78, not greater than.»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
A motorcycle that usually sells for $400 is marked down to $300. What is the markdown percent?
Answer:
25%
Step-by-step explanation:
The cost of a large cake at a bakery is $21.00. The cost of a small cake is
$8.25. The bakery also charges a sales tax of 8.25% and a delivery cost of
$10.50 for each order. The following expression represents the cost of an
(1) order
1.0825(21x + 8.25y) + 10.5
What does the term (21x + 8.25y) represent?
A А
the total cost of the order before delivery
the total delivery cost of the order
B
the total cost of the large cakes ordered
the subtotal cost of all the cakes ordered
before tax and delivery
Answer:
The Subtotal cost of all the cakes before tax and delivery
Step-by-step explanation:
(21x+8.25y)
21 is the price of 1 large cake and X is the number of cakes they want to purchase not counting tax and delivery fee.
8.25 is the price of 1 small cake and Y is the number of cakes they want to purchase not counting tax and delivery fee.
Which graph represents a function?
Answer:
The 4th graph represents a function
Step-by-step explanation:
trust bro
4th graph is a function
Option D is the correct answer
The sales tax for an item is 8%. The sales tax for an item that costs $130.19 is
Answer:
Step-by-step explanation:
Answer:
The sale tax is $10.42
