Answer:
[tex](x-4)(x^2+6)[/tex]
Step-by-step explanation:
x³-4x²+6x-24 is our equation
Once we factor it we get
[tex](x-4)(x^2+6)[/tex]
If z varies directly as x and inversely as y and is equal to 4 when x and y have the values 12 and 8 respectively, what is the value of z when x is equal to 6/7 and y is equal to 5/28?
Answer:
[tex]z = \frac{2}{7} [/tex] when x= [tex] \frac{6}{7} [/tex],
z= 179.2 when y= [tex] \frac{5}{28} [/tex]
Step-by-step explanation:
Let's start by writing out the two general equations for z.
Since z varies directly with x,
z= kx, where k is a constant.
Since z varies inversely with y,
[tex]z = \frac{k}{y} [/tex], where k is a constant.
When x= 12, z= 4,
4= k(12)
12k= 4
k= 4 ÷12
k= ⅓
∴ z= ⅓x
When x=[tex] \frac{6}{7} [/tex],
[tex]z = \frac{1}{3} ( \frac{6}{7} )[/tex]
[tex]z = \frac{2}{7} [/tex]
When y= 8, z= 4,
[tex]4 = \frac{k}{8} [/tex]
k= 4(8)
k= 32
[tex]∴z = \frac{32}{y} [/tex]
When y= [tex] \frac{5}{28} [/tex],
[tex]z = 32 \div \frac{5}{28} [/tex]
[tex]z = 32 \times \frac{28}{5} [/tex]
z= 179.2
Out of 120 customers asked at a restaurant, 38 rounded their bill up to the next whole dollar and donated the difference to the local Children's Hospital. How many consecutive customers must round up the bills so that the percentage of people who donated increases to 50%?
A. 44 customers
B. 40 customers
C. 36 customers
D. 32 customers
Using proportions, it is found that 44 consecutive customers must round up the bills so that the percentage of people who donated increases to 50%, so option A is correct.
A proportion is the number of desired outcomes divided by the number of total outcomes.
Considering that 38 out of 120 customers rounded their bill up, with x customers added, the proportion will be of 38 + x out of 120 + x.
The desired proportion is 0.5, hence:
[tex]\frac{38 + x}{120 + x} = 0.5[/tex]
[tex]38 + x = 60 + 0.5x[/tex]
[tex]0.5x = 22[/tex]
[tex]x = \frac{22}{0.5}[/tex]
[tex]x = 44[/tex]
44 customers, so option A.
A similar problem is given at https://brainly.com/question/20571459
$200 is shared between Bill and Ann. Ann’s share is $50 more than Bill’s share. Calculate the size of each of their shares.
First subtract the difference between the two:
200 - 50 = 150
Now divide that by 2:
150/2 = 75
Bills share is $75
Now add the $50 to 75 to get Ann's share:
75 + 50 = $125
Ann's share is $125
Bill's share is $75
Ana is playing a quiz game and needs more than 500 points to advance to the next level. She earns 18 points for each correct answer loses 6 points foWhat is an inequality that represents all the possible combinations of c, the number of correct answers, and w, the number of incorrect answers that Ana can get and move to the next level?
if the words after " 6 points fo" is "r each incorrect answer" then the answer is
18c - 6w > 500
explanation:
if she answers one correct, she'll get 18 points, so if she gets 18 correct, she'll get 18c points, same goes for each she gets incorrect but loses 6 points is +-6w, or simplified, -6w
need help asap PLS HURRY
logx=(logx)^2
find the value of x without using calculator
Answer:
x = 1
Step-by-step explanation:
log(1) = 0
log(1) = [tex]log(1)^{2}[/tex]
0 = [tex]0^{2}[/tex]
0 = 0
Solve for x. x+12√=x√+2
[tex]x = - \frac{2 \sqrt{3} + 12 }{11} [/tex]
hope it helps
see the attachment for explanation
[tex] \: [/tex]
I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 30 miles per hour instead, then I would have arrived 25 minutes later. How many miles did I drive?
Step-by-step explanation:
x = number of hours driven
25 minutes = 5/12 hour
remember,
1 hour = 60 Minuten
5 minutes = 60/12 minutes = 1/12 hour
25 minutes = 5×5 minutes = 5/12 hour
x hours × 40 miles/hour = (x + 5/12) hours × 30 miles/hour
the dimensions "hour" eliminate each other from the top and the bottom of the fractions leaving only miles. and the miles must be the same either way.
40x = (x + 5/12)×30 = 30x + 150/12
10x = 150/12
x = 15/12 = 5/4 hours
40 miles/hour × 5/4 hours = 40×5/4 miles = 10×5 = 50 miles.
I drove 50 miles.
The area of a triangular flower bed in the park has an area of
120 square feet. The base is six feet shorter than three times the height. What are the base and height of the triangle?
Answer:
b = 24 ft
h = 10 ft
Step-by-step explanation:
120 = ½hb
120 = ½h(3h - 6)
240 = h(3h - 6)
240 = 3h² - 6h
80 = h² - 2h
0 = h² - 2h - 80
0 = (h - 10)(h + 8)
h = 10 ft or -8 ft
we ignore -8 as it makes no sense for a triangle side length.
b = 3(10) - 6 = 24 ft
In 2013, the Public Religion Research Institute conducted a survey of 1,033 adults, 18 years of age or older, in the continental United States. One of the questions on their survey was as follows:
On any given Sunday, are you more likely to only be in church, more likely to only be watching football, doing both, or doing neither?
(a) To only be in church [269 respondents selected this answer]
(b) To only be watching football [175 respondents selected this answer]
(c) Doing both [217 respondents selected this answer]
(d) Doing neither [372 respondents selected this answer]
Create a 95% confidence interval to estimate the actual percentage of adults in the U.S., aged 18 and older, that are "likely" to ONLY be in church on any given Sunday.
Using the z-distribution, it is found that the 95% confidence interval to estimate the actual percentage of adults in the U.S., aged 18 and older, that are "likely" to ONLY be in church on any given Sunday is (23.36%, 28.72%).
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
269 out of 1033 respondents said they were likely to only be in church, hence:
[tex]n = 1033, \pi = \frac{269}{1033} = 0.2604[/tex]
95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2604 - 1.96\sqrt{\frac{0.2604(0.7396)}{1033}} = 0.2336[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2604 + 1.96\sqrt{\frac{0.2604(0.7396)}{1033}} = 0.2872[/tex]
As a percentage:
0.2336 x 100% = 23.36%
0.2872 x 100% = 28.72%
The 95% confidence interval to estimate the actual percentage of adults in the U.S., aged 18 and older, that are "likely" to ONLY be in church on any given Sunday is (23.36%, 28.72%).
A similar problem is given at https://brainly.com/question/25743435
A proportional relationship is shown in the table below
X 0 .3 .6 .9 1.2
Y 0 1 2 3 4
Can someone help me on theses?
4) A teacher has an annual income of $51,750. The income tax the teacher has to pay is 7%. What is the amount of income tax in dollar and cents the teacher has to pay?
A) $3,448.25
B) $3,622.50
C) $3,891.10
D) $3,933.01
9514 1404 393
Answer:
B) $3,622.50
Step-by-step explanation:
To find the tax, multiply the income by the tax rate:
$51,750 × 0.07 = $3,622.50
I need to know how to subtract fractions 4 2/3 - 3/4
Answer: The answer would be 3.91666666667
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{4 \dfrac{2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{4\times3+2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{12 + 2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{14}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{56}{11} - \dfrac{9}{12}}[/tex]
[tex]\mathsf{= \dfrac{14\times4}{12 - 0}}[/tex]
[tex]\mathsf{= \dfrac{56 - 9}{12}}[/tex]
[tex]\mathsf{= \dfrac{47}{12}}[/tex]
[tex]\mathsf{= 3 \dfrac{11}{12}}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: }\huge\boxed{\\\mathsf{\dfrac{47}{12} \ or\ 3 \dfrac{11}{12}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
In a recent tennis tournament, women playing singles matches used challenges on 133 calls made by the line judges. Among those challenges, 31 were found to be successful with the call overturned. a. Construct a 90% confidence interval for the percentage of successful challenges. b. Compare the results from part (a) to this 90% confidence interval for the percentage of successful challenges made by the men playing singles matches: 20.9%
Using the z-distribution, it is found that the 90% confidence interval for the percentage of successful challenges is (17.28, 29.34).
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
31 out of 133 challenges were successful, hence:
[tex]n = 133, \pi = \frac{31}{133} = 0.2331[/tex]
90% confidence level, hence [tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 - 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.1728[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 + 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.2934[/tex]
As percentages:
0.1728 x 100% = 17.28%
0.2934 x 100% = 29.34%
The 90% confidence interval for the percentage of successful challenges is (17.28, 29.34).
A similar problem is given at https://brainly.com/question/16807970
Please tell me how much can 6 go into 14 without going over 14
Help please on part b
Answer:
-0.045
Step-by-step explanation:
you first take the derivate of A(t)
A'(t)=1.4e^-0.05t X (-0.05)
A'(t)=-0.07e^-0.05t
so when t=0
amount remaining is -0.07e^-0.05(0) ---- e^0 = 1
so its -0.07
when t=9
do the same thing,
-0.07e^-0.05(9) ---use calculator
-0.045
What is the value of v?
Answer:
34 degrees
Step-by-step explanation:
If you know the 2 interior angles of a triangle, you can find the 3rd.
This is useless since this is a right triangle.
In this case:
v + 46 = 90
v = 34 degrees
You are welcome!
Kayden Kohl
8th Grade Student
The population in millions of a city t years after 1990 is given by the equation p(t) = 2.9+0.08t in this function
Answer:
The answer would be 2.9 million is the population of the city in 1990 and 0.08 million is the increase per year in the population.
Hope it help and if it its correct please give brainliest
Stay Safe And Healthy
Thank You
Please help! Will give 50 points!!
Answer:
- 5 | - 1 | 3 | 7Step-by-step explanation:
Given function:
y = 2x + 3Complete table by finding y values:
x = - 4 ⇒ y = 2*(-4) + 3 = - 8 + 3 = - 5x = - 2 ⇒ y = 2*(-2) + 3 = - 4 + 3 = - 1x = 0 ⇒ y = 2*0 + 3 = 0 + 3 = 3x = 2 ⇒ y = 2*2 + 3 = 4 + 3 = 7Hello, can you help me?, thank you
Answer:105216
Step-by-step explanation:17,536*6=105216
Answer:
105,216
Step-by-step explanation:
17,536*6
Please help
Solve.
(5√5)^−2x+1 = 1/5 ⋅ 125^x−3
Enter your answer in the box. Enter any fraction as a simplified fraction.
Step-by-step explanation: (5√5)−2x+1=
1
5
(125x)−3
0.008x+1=
1
5
(125x)−3
Step 1: Flip the equation.
1
5
(125x)−3=0.008x+1
Step 2: Add 3 to both sides.
1
5
(125x)−3+3=0.008x+1+3
1
5
(125x)=0.008x+4
Step 3: Divide both sides by 1/5.
1
5
(125x)
1
5
=
0.008x+4
1
5
125x=0.04x+20
The value of x is 46.
What are Exponents and power?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
The number of times a number is multiplied by itself is defined by the exponent. The power is an expression that displays the same number or factor being multiplied repeatedly.
Given:
[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 125^{x-3}[/tex]
ow, using exponents and powers
[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 125^{x-3}[/tex]
[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 5 ^{3(x-3)\\[/tex]
[tex](5\sqrt{5} )^{-2x+1 }= 5^{3x - 9 - 1}[/tex]
[tex](5\sqrt{5} )^{-2x+1 }= 5^{3x -10}[/tex]
[tex]5^{3/2(-2x+ 1)}= 5^{3x - 10}[/tex]
[tex]5^{-x+ 3/2}= 5^{3x -10}[/tex]
Now, Comparing
-x+ 3/2 = 3x- 10
-x - 3x = -10 - 3/2
-4x = -23/2
x= 46
Hence, the value of x is 46.
Learn more about Exponents and powers here:
https://brainly.com/question/15722035
#SPJ2
A
Triangle ABC is right-angled at A, and AD is the altitude from A to the hypotenuse BC.
Find x
Answer:
Step-by-step explanation:
5 x 6:30
Use the number line to answer the question below:
<—A——————-B————C—->
If AB = 7x - 24 and BC = 6x - 2, what is the value of AC?
a. 13x - 22
C. 13x - 26
b. 33
d. 46
Work Shown:
AC = AB + BC
AC = (7x-24) + (6x - 2)
AC = (7x+6x) + (-24-2)
AC = 13x - 26
This works because segment AC is split up into two parts AB and BC which don't overlap. Refer to the segment addition postulate.
A hummingbird lives in a nest that is 12 meters high in a tree. The hummingbird flies 15
meters to get from its nest to a flower on the ground. How far is the flower from the base of
the tree?
Answer:
The flower is 9 meters from the base of the tree.
Step-by-step explanation:
Use the Pythagorean theorem to solve. We are given the length of one leg and the length of the hypotenuse of a right triangle.
[tex]a^{2} +b^{2} =c^{2}[/tex]
where a and b are the legs, and c is the hypotenuse.
Plug in the given values and solve:
[tex]x^{2} +12^{2} =15^{2} \\x^{2} +144=255\\x^{2} =81\\x=9[/tex]
The flower is 9 meters from the base of the tree.
Solve please
May God bless you
Answer:
We will use a Pythagorean identity and alegbra to prove this.
sin^2 + cos^2 = 1, dividing by cos^2 gives
tan^2 + 1 = sec^2.
Now, breaking down the fraction into parts and simplifying gives:
(1-sin^4)/cos^4 = 1/cos^4 - sin^4/cos^4 = sec^4 - tan^4
Now use difference of squares factoring from alegbra.
= (sec^2 + tan^2)*(sec^2 - tan^2)
By rewriting our Pythagorean identity to
sec^2 - tan^2 = 1 and tan^2 = sec^2 - 1,
we can finish the problem.
= (sec^2 + tan^2) * 1 = sec^2 + tan^2
= sec^2 + (sec^2 - 1) = 2*sec^2 - 1.
What is 3/4+1 2/3+1/2=
Answer:
Exact Form:
35/12
Decimal Form:
2.916- (6 goes on)
Mixed Number Form:
2 11/12
If a shirt cost $60 is on sale for 50% off and you have another offer that gives you an additional 20% off the sale price does that mean you get a total of 70% off show your work to justify your answer
Answer:
No
Step-by-step explanation:
50 % off $60 =$30
20% off $30 =$6
But 70% =42
Therefore it's not the same as 70%
What is the slope of the line that passes through the points (6, -10) and (3, -13)?
Write your answer in simplest form.
[tex](x_1, y_1) = (6,-10),~~ (x_2, y_2) = (3,-13)\\\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-13 +10}{3 -6} =\dfrac{-3}{-3} =1[/tex]
The price of an item has risen to $343 today. Yesterday it was $140. Find the percentage increase.
Answer:
145% increase
Step-by-step explanation:
343 - 140 = 203
203/140 = 1.45
1.45 x 100 = 145