A rectangular garden is 5 ft longer than it is wide. Its area is 1800ft^2. What are its dimensions?
Answer:
The dimensions are 45 feet by 40 feet.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A=w\ell[/tex]
Where w is the width and l is the length.
The length is five feet longer than the width. Thus, we can write that:
[tex]\ell = w+5[/tex]
The total area is 1800 square feet. Substitute:
[tex]1800=w(w+5)[/tex]
Solve for w. Distribute:
[tex]w^2+5w=1800[/tex]
Subtract 1800 from both sides:
[tex]w^2+5w-1800=0[/tex]
Factor. We can use 45 and -40. Hence:
[tex]\displaystyle (w+45)(w-40)=0[/tex]
Zero Product Property:
[tex]w+45=0\text{ or } w-40=0[/tex]
Solve for each case:
[tex]\displaystyle w=-45\text{ or } w=40[/tex]
Since the width cannot be negative, we can ignore the first solution.
So, the width is 40 feet. Since the length is five feet longer, the length is 45 feet.
The dimensions are 45 feet by 40 feet.
-11 + 4(3+1) + 3(5-9) + 7(6-8) + 25
Answer:
4
Step-by-step explanation:
-11 + 4(3+1) + 3(5-9) + 7(6-8) + 25
-11+4*4+3*-4+7*-2+25
-11+16+-12+-14+25
4
Show process!!!!!!!
Thank you
======================================================
Work Shown:
We can apply the law of cosines
a^2 = b^2+c^2-2*b*c*cos(A)
(sqrt(5))^2 = (sqrt(2))^2+(3)^2-2*(sqrt(2))*(3)*cos(A)
5 = 2+9-6*(sqrt(2))*cos(A)
5 = 11-6*(sqrt(2))*cos(A)
11-6*(sqrt(2))*cos(A) = 5
-6*(sqrt(2))*cos(A) = 5-11
-6*(sqrt(2))*cos(A) = -6
(sqrt(2))*cos(A) = -6/(-6)
(sqrt(2))*cos(A) = 1
cos(A) = 1/(sqrt(2))
cos(A) = sqrt(2)/2
A = 45 degrees
Use the unit circle for the last step.
Interestingly, this triangle has only one angle that is a whole number. The other two angles are approximate decimal values.
Identify the quantities that are equivalent to 250 meters.
Ratio Conversion Table
kilometer (km) : meter (m) 1 : 1,000
meter (m) : centimeter (cm) 1 : 100
centimeter (cm) : millimeter (mm) 1 : 10
Answer:
1. Convert all measurements to meters:
2.5km * 1,000 = 2,500m;.250km * 1,000 = 250m; 2,500cm / 100 = 25m
25,000cm / 100 = 250m; 250mm / 1,000 =.25m
2.) Compare the converted measurements. Therefore, the quantities that are equivalent to 250m are:
.250km; 25,000cm
Step-by-step explanation:
Write down the equation that could be a correct equation for linear regression prediction function?
If the question meant that we should write a linear prediction function ;
Answer:
y = bx + c
Step-by-step explanation:
The equation for a linear regression prediction function is stated in the form :
y = bx + c
Where ;
y = Predicted or dependent variable
b = slope Coefficient
c = The intercept value
x = predictor or independent variable
Therefore, the Linear function Given represents a simple linear model for one dependent variable, x
b : is the slope value of the equation, whuch represents a change in y per unit change in x
A large container holds 4 gallons of chocolate milk that has to be poured into bottles. Each bottle holds 2 pints.
If the ratio of gallons to pints is 1: 8,
bottles are required to hold the 4 gallons of milk.
Answer:
64 Bottles
Step-by-step explanation:
that is the procedure above
help me guys, I really need your help
Answer:
The answer should be like this;
a) A-B
b) BUC
c) C-A
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ツ
Answer pls:) I would really appreciate it
Answer:
1. C
2. B
3 A
4. A
Step-by-step explanation:
#1
Brady starts off with 12 coins
And buys 6 more coins every year
So add 6 to find number of coins he will have the next year until we've done it five times ( because we want to find how many he will have after 5 years )
12 ( 1st year )
Add 6
12 + 6 = 18 ( 2nd year )
Add 6
18 + 6 = 24 ( 3rd year )
Add 6
24 + 6 = 30 ( 4th year )
Add 6
30 + 6 = 36 ( 5th year )
By the fifth year he will have 36 coins and the sequence would be
12, 18, 24, 30, 36
Which corresponds with answer choice C
2
15, 19, 23, 27, ?
We want to find the next term
To do so we must find the common difference
We can do this by subtracting the last given term by the term before it
27 - 23 = 4
Just to clarify we can do the terms before those
19 - 15 = 4
So the common difference is 4
Now to find the next term we simply add 4 to the last given term
27 + 4 = 31
The next term would be 31
3. Cumulative property of addition states that you can add any 3 numbers in a different order and they will be the same
a + b + 2 = 2 + a + b
Same variables and numbers just different order
Therefore this is an example of cumulative property of addition
4. The GCF ( greatest common factor ) is the greatest number that the two numbers can be divided by
18a and 24ab
Factors of 18
2 , 9 , 6, 3 , 1 and 18
Factors of 24
24, 1, 2, 12, 6, 4, 3 and 8
The greatest factor that both 18 and 24 have is 6
The GCF would be 6a ( not 6 ) because both numbers share a common variable (a) ( 18a , 24ab )
Find the missing term in the pattern.
Answer:
20
Step-by-step explanation:
6 + 2 = 8
8 + 3 = 11
11 + 4 =15
15 + 5 =20
Answer:
20
Step-by-step explanation:
the pattern is increase the number by one more than the increase before. so 6,8=2 greater
8-11=3 greater. 11-15=4 greater. so, 15+5=20 (with this answer being 5 greater continuing the pattern.)
What is the area of 4cm×7cm×8cm
Answer:
[tex]224cm^3\\[/tex]
Step-by-step explanation:
[tex]4cm*7cm*8cm=[/tex]
[tex]=224cm^3[/tex]
Hope this is helpful.
LWH=A
Plug in the numbers:
4*7*8=224^2
The area would be 224cm^2.
Which of the following indicates that Triangle ABC and Triangle DEF are similar?
Answer:
D
Step-by-step explanation:
The symbol ~ means similarity (same shapes, not same size)
Given that m∠abc=70° and m∠bcd=110°. Is it possible (consider all cases): Line AB intersects line CD?
The line AB and CD are parallel. Then it is impossible that the line AB intersects the line CD.
What are parallel lines?When the distance between the lines is constant, then the lines are called parallel lines. The lines do not intersect when they are separated from each other. And the slope of the lines is equal.
Given that ∠ABC = 70° and ∠BCD = 110°.
Then the line AB and the line CD makes the same angle with the line BC.
Hence, the line AB and CD are parallel.
Then it is impossible that the line AB intersects the line CD.
More about the parallel lines link is given below.
https://brainly.com/question/16701300
#SPJ1
What is the probability a person admitted to the hospital is paid a malpractice claim (to decimals)
Full question:
Astudy of 31,000 hospital admissions in New York State found that 4% of the admissions
led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in
death, and one-fourth were caused by negligence. Malpractice claims were filed in one out
of 7.5 cases involving negligence, and payments were made in one out of every two claims
What is the probability a person admitted to the hospital is paid a malpractice claim (to decimals)
Answer:
Explanation:
Since 4% of admissions lead to treatment-caused injuries, we have 4/100×31000= 1240 treatment caused injuries for every 31000 people admitted
1/7 resulted in death = 1/7×1240= 177 people die for every 1240 treatment caused injuries
1/4 from negligence= 1/4×1240= 310 people get treatment caused injuries from negligence for every 1240 people
Malpractice claims in one of out of 7.5 cases of negligence= 13.3% of negligence cases= 0.1333×310= 41 claims for every 1240 people with treatment caused injuries
Payments were made in one out of every two claims, therefore payments for claims =50% of 41 cases of negligence= 21 payments(approximately) for every 1240 people with treatment caused injuries
Probability= number of favorable outcomes /total number of outcomes
Probability that a person admitted into the hospital will be paid a claim= 21/31000= 0.000677
find the h.c.f. if 84 and 72
Answer:
12
Step-by-step explanation:
First lets list all the factors of these numbers
72: 1,2 3,4,6,8,9,12,18,24,36,72
84: 1 , 2 , 3 ,4 , 6 , 7 , 12 , 14 , 21 , 28 , 42 , 84
Now lets find the biggest number that is a factor of both 84 and 72
as we can see the highest number that is the factor of both 84 and 72 is 12
12 is the hcf
M H To determine the number of deer in a game preserve, a conservationist catches 412 deer, tags them and lets them loose. Later, 316 deer are caught, 158 of them are tagged. How many deer are in the preserve?
Answer:
There are 824 deer in the preserve.
Step-by-step explanation:
Since to determine the number of deer in a game preserve, a conservationist catches 412 deer, tags them and lets them loose, and later, 316 deer are caught, 158 of them are tagged, to determine how many deer are in the preserve you must perform the following calculation:
316 = 100
158 = X
158 x 100/316 = X
50 = X
50 = 412
100 = X
824 = X
Therefore, there are 824 deer in the preserve.
find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Find the associated radius of convergence R. f(x) = 6(1 − x)−2 Step 1 The Maclaurin series formula is f(0) + f '(0)x + f ''(0) 2! x2 + f '''(0) 3! x3 + f (4)(0) 4! x4 + .
Answer:
= ∑ 6*n*x^n-1
Radius of convergence = 1
Step-by-step explanation:
f(x) = 6(1-x)^-2
Maclaurin series can be expressed using the formula
f(x) = f(0) + f '(0)x + f ''(0)/ 2! (x)^2 + f '''(0)/3! (x)^3 + f (4)(0) 4! x4 + .
attached below is the detailed solution
Radius of convergence = 1
The Maclaurin series for f(x) = 6 / (1 - x )^2 = ∑ 6*n*x^n-1 ( boundary ; ∞ and n = 1 )
Factor 2x^2+15x+25. Rewrite the trinomial with the x-term expanded,using the two factors. Then, group the first two and last two terms together and find the GCF of each.
Answer:
[tex][x + 5][2x+ 5][/tex]
Step-by-step explanation:
Given
[tex]2x^2 + 15x + 25[/tex]
Required
Factorize
Expand the x term
[tex]2x^2 + 5x + 10x+ 25[/tex]
Group into 2
[tex][2x^2 + 5x] + [10x+ 25][/tex]
Take the GCF of each group
[tex]x[2x + 5] + 5[2x+ 5][/tex]
Factor out 2x + 5
[tex][x + 5][2x+ 5][/tex]
What is the slope of (-4,1) and (-1,3)
Answer:
slope is 2÷3 of giving line points
A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 57% C: Scores below the top 43% and above the bottom 19% D: Scores below the top 81% and above the bottom 5% F: Bottom 5% of scores Scores on the test are normally distributed with a mean of 66.5 and a standard deviation of 9.9. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
Answer:
The minimum score required for an A grade is 80.
Step-by-step explanation:
According to the Question,
Given That, A philosophy professor assigns letter grades on a test according to the following scheme.A: Top 12% of scores
B: Scores below the top 12% and above the bottom 57%
C: Scores below the top 43% and above the bottom 19%
D: Scores below the top 81% and above the bottom 5%
F: Bottom 5% of scores Scores on the test
And The normally distributed with a mean of 66.5 and a standard deviation of 9.9.
Now,
In a set with mean and standard deviation, the Z score of a measure X is given by Z = (X-μ)/σwe have μ=66.5 , σ=9.9
Find the minimum score required for an A grade.Top 12%, so at least the 100-12 = 88th percentile, which is the value of X when Z has a p-value of 0.88. So it is X when Z = 1.175.
⇒ Z = (X-μ)/σ
⇒ 1.175×9.9 = X-66.5
⇒ X=78.132
Rounding to the nearest whole number, the answer is 80.
The minimum score required for an A grade is 80.
Write the quadratic equation in standard form:
3x2 – 3x = 11
Answer:
[tex]3x^{2} -3x-11 = 0[/tex]
Step-by-step explanation:
A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective. Is it fair to reject the manufacturer's claim based on this observation?
Answer:
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Step-by-step explanation:
A manufacturer of nails claims that only 4% of its nails are defective.
At the null hypothesis, we test if the proportion is of 4%, that is:
[tex]H_0: p = 0.04[/tex]
At the alternative hypothesis, we test if the proportion is more than 4%, that is:
[tex]H_a: p > 0.04[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
4% is tested at the null hypothesis
This means that [tex]\mu = 0.04, \sigma = \sqrt{0.04*0.96}[/tex]
A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.
This means that [tex]n = 20, X = 0.1[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.1 - 0.04}{\frac{\sqrt{0.04*0.96}}{\sqrt{20}}}[/tex]
[tex]z = 1.37[/tex]
P-value of the test and decision:
Considering an standard significance level of 0.05.
The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.
Looking at the z-table, z = 1.37 has a p-value of 0.9147
1 - 0.9147 = 0.0853
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Answer:
Considering an standard significance level of 0.05.
The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.
Looking at the z-table, z = 1.37 has a p-value of 0.9147
1 - 0.9147 = 0.0853
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Step-by-step explanation:
Suppose that 70% of all voters prefer Candidate A. If 4 people are chosen at random for a poll, what is the probability that exactly 1 of them favor Candidate A?
Answer:
0.0756
Step-by-step explanation:
p(success), p = 70% = 0.7
Nunber of trials, n = 4
q = 1 - p = 1 - 0. 7 = 0.3
x = 1
The question meets the requirements of a binomial probability distribution :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 1) = 4C1 * 0.7^1 * 0.3^(4-1)
P(x = 1) = 4C1 * 0.7 * 0.3^3
P(x = 1) = 4 * 0.7 * 0.027
P(x = 1) = 0.0756
what's the value of the function f(x)= 2x+5 if x=3
Answer:
f(x) = 2(3) + 5
= 6 + 5 = 11
y = 11
x = 3
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
Please help solve and explain this
can you put the whole question here
Respond to each of the four questions.
Describe the steps to graphing a linear equation. Be sure to provide an example to illustrate your description.
Describe the steps to graphing a quadratic equation. Be sure to provide an example to illustrate your description.
Describe how to solve a linear equation. Be sure to provide an example to illustrate your description.
Describe how to solve a quadratic equation. Be sure to provide an example to illustrate your description.
Answer:hello
Step-by-step explanation:
1+1
Please explain :)
Expand 5x(x+2)
Thanks :)
Answer:
[tex] {5 x }^{2} +10x[/tex]
Step-by-step explanation:
[tex]5x(x+2)[/tex]
[tex]5x \times x+5x \times 2[/tex]
[tex]5(x \times x)+5x \times 2[/tex]
[tex]5 {x}^{2} +5x \times 2[/tex]
[tex]5 {x}^{2} + 10x[/tex]
Hope it is helpful....Determine whether the following fractions terminate in their decimal form. Show all work and explain your reasoning. YOU CAN NOT USE A CALCULATOR. Try not using long division.
Answer:
8/22: this fraction will NOT terminate
189/270: this fraction WILL terminate
Step-by-step explanation:
I saw in the question that it says to solve the question by demonstrating the method discussed in class. I don't know what's the method you were taught, but I'll explain how I solved it.
When a fraction is in its simplest form, write out the prime factors of the denominator. If the denominator has 2s and/or 5s, the fraction WILL terminate in their decimal form.
8/22 in its simplest form is 4/11:
The only prime factors of the denominator, 11, are 1 and 11. There are no 2s and/or 5s present, so this fraction will NOT terminate.
189/270 in its simplest form is 7/10.
The prime factors of 10 are 2 and 5, meaning that this fraction WILL terminate.
Hope it helps (●'◡'●)
3x=4(c-d)/d make d the subject
Answer:
[tex]d = \frac{4c}{3x + 4} [/tex]
Step-by-step explanation:
[tex]3x = \frac{4(c - d)}{d} [/tex]
Multiply both sides by d:
[tex]3xd = 4(c - d)[/tex]
Expand:
[tex]3xd = 4c \: - 4d[/tex]
+4d on both sides:
[tex]3xd + 4d = 4c[/tex]
Factorise d out of the left-hand side:
[tex]d(3x + 4) = 4c[/tex]
Divide both sides by (3x +4):
[tex]d = \frac{4c}{3x + 4} [/tex]
Find the next number of the series 563, 647, 479, 812
Answer:
146
Step-by-step explanation:
next number is the last -666
True/False Questions - one attempt tor each question
If f is a decreasing function on an interval, then f'(x) > 0 on that interval.
True
False
Submit Question
Answer:
False
Step-by-step explanation:
f'(x) would be a negative number. Hence less than zero.
