Answer:
50% chance
Step-by-step explanation:
4 * 50% = 2
A box is 30 inches wide, 16 inches long, and 14 inches high. To the nearest cubic inch, what is the volume of the box?
Answer:
6720 in ^3
Step-by-step explanation:
Volume = length * width * height
= 30*16*14
=6720 in ^3
Please answer this correctly without making mistakes
Answer:
105/4 or 26.25 mi
Step-by-step explanation:
hillsdale to fairfax 8 7/8 = 71/8
fairfax to yardley = 17 3/8 = 139/8
71/8 + 139/8 = 105/4 or 26 2/8
(a + b + c) power of 10 - abc
Tip
A=1
B=2
C= -3
[tex]\\ \rm\longmapsto (a+b+c)^{10}-abc[/tex]
[tex]\\ \rm\longmapsto (1+2-3)^{10}-(1)(2)(-3)[/tex]
[tex]\\ \rm\longmapsto (3-3)^{10}+6[/tex]
[tex]\\ \rm\longmapsto 0^{10}+3[/tex]
[tex]\\ \rm\longmapsto 0+3[/tex]
[tex]\\ \rm\longmapsto 3[/tex]
(a+b+c)^10-abc
= (1+2-3)^10-(1×2×-3)
= 0- (-6)
=6 answer.....
Lena is comparing offers from two banks on checking accounts that include debit cards. Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions. Bank B charged a $5 monthly fee for a checking account and debit card, plus
$ 0.50 for each transaction.
Suppose Lena makes 35 transactions in a given month.
How much would she pay at each bank for the given month?
Bank A
Bank B
For the given month, which bank is cheaper and by how much?
Bank A. is cheaper than Bank B by $
or
Bank B is cheaper than Bank A by $
Answer:
Bank A spending= $20
Bank B spending= $22.5
Bank A is cheaper with $2.5
Step-by-step explanation:
Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions.
Sheade 35 transactions.
Total charges from bank A
= $20 monthly
Bank B charged a $5 monthly fee for a checking account and debit card, plus
$ 0.50 for each transaction.
She made 35 transactions.
Total charges on bank B= $5 + (0.5)35
Total charges on bank B= $5+17.5
Total charges on bank B= $22.5
In a study of 24 criminals convicted of antitrust offenses, the average age was 60 years, with a standard deviation of 7.4 years. Construct a 95% confidence interval on the true mean age. (Give your answers correct to one decimal place.)___ to____ years
Answer: 56.9 years to 63.1 years.
Step-by-step explanation:
Confidence interval for population mean (when population standard deviation is unknown):
[tex]\overline{x}\pm t_{\alpha/2}{\dfrac{s}{\sqrt{n}}}[/tex]
, where [tex]\overline{x}[/tex]= sample mean, n= sample size, s= sample standard deviation, [tex]t_{\alpha/2}[/tex]= Two tailed t-value for [tex]\alpha[/tex].
Given: n= 24
degree of freedom = n- 1= 23
[tex]\overline{x}[/tex]= 60 years
s= 7.4 years
[tex]\alpha=0.05[/tex]
Two tailed t-critical value for significance level of [tex]\alpha=0.05[/tex] and degree of freedom 23:
[tex]t_{\alpha/2}=2.0687[/tex]
A 95% confidence interval on the true mean age:
[tex]60\pm (2.0686){\dfrac{7.4}{\sqrt{24}}}\\\\\approx60\pm3.1\\\\=(60-3.1,\ 60+3.1)\\\\=(56.9,\ 63.1)[/tex]
Hence, a 95% confidence interval on the true mean age. : 56.9 years to 63.1 years.
let p and p+2 be prime numbers (i.e they are twin primes) with p>3. Show that 6|(p+1)
from the well known theorem that, primes are multiple of 6 ±1 ( eg 5,7,11,13,17,19...)
and one of them has [tex]-1[/tex] and other has $+1$ from the multiple of 6
let , $p=6n-1$, so $p+2=6n+1$
$\implies p+1=6n$
$\therefore 6|(p+1)$
QED
Please help!!! On my hw
Answer:
c(X)=R(X)
125x+18000=215x
18000=215x-125x
18000=90x (divede both sides by 90)
X=200
Express as a trinomial (3x+8) (x+10)
Answer:
[tex]3x^{2} +38x+80[/tex]
Step-by-step explanation:
Hello!
A trinomial is a expression consisting of three different terms
To turn this into a trinomial we multiply everything to each other
3x
3x * x = [tex]3x^{2}[/tex]
3x * 10 = 30x
8
8 * x = 8x
8 * 10 = 80
Now we put them all together in an equation
[tex]3x^{2} +30x+8x+80[/tex]
Combine like terms
[tex]3x^{2} +38x+80[/tex]
The answer is [tex]3x^{2} +38x+80[/tex]
Hope this helps!
Draw the image of ABC under dilation whose center is P and scale factor is 4.
Answer:
Step-by-step explanation:
Let the point P is origin (0, 0), segment AB lies on the x-axis and segment PC on the y-axis,
Coordinates of A, B and C will be (1, 0), (2, 0) and (0, 2).
When triangle ABC is dilated by a scale factor 4 about the origin,
Rule for dilation;
(x, y) → (4x, 4y)
New coordinates of the points A, B and C will be,
A(1, 0) → A'(4, 0)
B(-2, 0) → B'(-8, 0)
C(0, 2) → C'(0, 8)
By plotting points A', B' and C' we can get the dilated image A'B'C'.
Dilation involves changing the size of a shape.
Assume point P is the center of origin, then we have the following coordinates of ABC
[tex]A = (1,0)[/tex]
[tex]B = (-2,0)[/tex]
[tex]C = (0,2)[/tex]
The scale factor (k) is given as:
[tex]k= 4[/tex]
So, the dilation rule is represented as:
[tex](x,y) \to (4 \times (x,y)[/tex]
Using the above dilation rule, the following coordinates represent the image of triangle ABC
[tex]A' = (4,0)[/tex]
[tex]B' = (-8,0)[/tex]
[tex]C = (0,8)[/tex]
See attachment for the image of the dilation.
Read more about dilation at:
https://brainly.com/question/8532602
Part of the population of 6,750 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 3 of them are infected. How many elk are likely to be infected?
Answer:
405
Step-by-step explanation:
We can use a ratio to solve
3 infected x infected
------------------ = ----------------
50 sampled 6750 population
Using cross products
3*6750 = 50x
Divide each side by 50
3*6750/50 = x
405
Answer:
Around 405 elk should be infected with the parasite.
Step-by-step explanation:
6,750/50=135
135 * 3 = 405
hope this helps :)
Travis has a budget of $300 that he can spend on perennial flowers and at least 6 annual flowers. Perennial flowers are 18 dollars per plant and annual flowers are 15 dollars per plant. Let x be the amount spent on perennial flowers, and let y be the amount spent on annual flowers. What system of inequalities describes this situation?
Answer:
18x + 15y ≤ 300x ≥ 0; y ≥ 6Step-by-step explanation:
Variables are defined in the problem statement.
18x +15y ≤ 300 . . . . total budget
y ≥ 6 . . . . . . . . . . . . minimum number of annuals
x ≥ 0 . . . . . number of perennials cannot be negative
This system of inequalities describes the situation.
Mary states, "If the diagonals of a parallelogramare congruent, then the
parallelogram is a rectangle." Decide if her statement is wue or false.
A. True
B. False
Answer:
True
Step-by-step explanation:
A rectangle is a plane figure with congruent length of opposite sides. Considering a rectangle ABCD,
AD ≅ BC (opposite side property)
AB ≅ CD (opposite side property)
<ABC = <BCD = <CDA = <DAC = [tex]90^{0}[/tex] (right angle property)
Thus,
<ABC + <BCD + <CDA + <DAC = [tex]360^{0}[/tex]
AC ⊥ BD (diagonals are perpendicular to each other)
AC ≅ BD (congruent property of diagonals)
Therefore, the parallelogram is a rectangle.
Describe each of the following values as (A) a discrete random variable, (B) a continuous random variable, or (C) not a random variable:
1. Exact weight of quarters now in circulation in the United States
2. Shoe sizes of humans
3. Political party affiliations of adults in the United States
A. 1.C
2.A
3.В
B. 1.B
2.A
3.С
C. 1.A
2.C
3.В
D. 1.A
2.В
3.С
Answer:
(1) B
(2) A
(3) C
Step-by-step explanation:
A random variable is a variable that denotes a set of all the possible outcomes of a random experiment. It is denotes by a single capital letter such as X or Y.
There are two types of random variables.
Discrete random variable: These type of random variable takes finite number of values, such as 0, 1, 2, 3, 4, ... For example, number of girl child in a neighborhood.Continuous random variable: These type of random variables takes infinite number of possible values. For example, the height, weight.(1)
Exact weight of quarters now in circulation in the United States.
The variable weight is a continuous variable.
Thus, the exact weight of quarters now in circulation in the United States is a continuous random variable.
(2)
Shoe sizes of humans.
The shoe size of a person are discrete and finite values.
Thus, the shoe sizes of humans are discrete random variables.
(3)
Political party affiliations of adults in the United States.
This variable is not a quantitative variable.
It is a qualitative variable.
Thus, the political party affiliations of adults in the United States is no random variable.
A salesperson earns $99 per day, plus a 9% sales commission. Find a function that
expresses her earnings as a function of sales, and use it to compute her earnings if the
total sales were $999. The salesperson would take home $___ for the day?
$188.00
$188.91
$188.99
$189.99
Answer:
$188.91
Step-by-step explanation:
$999*.09=$89.91
$89.91+$99=$188.91
What is the perimeter of half of a circle with a diameter of 14 inches?
Answer:
35.991
Step-by-step explanation:
A certain dataset of systolic blood pressure measurements has a mean of 80 and a standard deviation of 3. Assuming the distribution is bell-shaped and we randomly select a measurement:
a) What percentage of measurements are between 71 and 89?
b) What is the probability a person's blood systolic pressure measures more than 89?
c) What is the probability a person's blood systolic pressure being at most 75?
d) We should expect 15% of patients have a blood pressure below what measurement?
e) Would it be unusual for 3 patients to have a mean blood pressure measurement of more than 84? Explain.
Answer:
Explained below.
Step-by-step explanation:
Let X = systolic blood pressure measurements.
It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].
(a)
Compute the percentage of measurements that are between 71 and 89 as follows:
[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]
[tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of measurements that are between 71 and 89 is 99.73%.
(b)
Compute the probability that a person's blood systolic pressure measures more than 89 as follows:
[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]
[tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]
Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.
(c)
Compute the probability that a person's blood systolic pressure being at most 75 as follows:
Apply continuity correction:
[tex]P(X\leq 75)=P(X<75-0.5)[/tex]
[tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]
Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.
(d)
Let x be the blood pressure required.
Then,
P (X < x) = 0.15
⇒ P (Z < z) = 0.15
⇒ z = -1.04
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]
Thus, the 15% of patients are expected to have a blood pressure below 76.9.
(e)
A z-score more than 2 or less than -2 are considered as unusual.
Compute the z score for [tex]\bar x[/tex] as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]
The z-score for the mean blood pressure measurement of 3 patients is more than 2.
Thus, it would be unusual.
An 8×8×8 cm cube was painted red, and then broken up into small cubes with side lengths of 1 cm. How many small cubes have none of their faces painted red?
Answer:
216
Step-by-step explanation:
If you just paint the surface of the cube, then the inside of the cube would not have any of their faces painted red.
Just looking at the cube from a side view, you would realize that there would be a smaller cube, 6 x 6 x 6 (not 7 since you have to account for both the top side and the bottom side), and so that is the answer, 6 ^ 3, which is 216.
Answer:
216
Step-by-step explanation:
8 * 8 * 8 = 512
8 * 8 = 64
Each face is 64 cubes, overlapping at the edges, with 6 faces total.
16 + 12 = 28 for each overlapping cube on each side
64 * 6 = 384
384 - 2(28) = 328
Top & Bottom dealt with, overlap from them is 56 units total, 14 units on top and bottom of each face..
64 - 14 = 50
50 * 2 = 100
Front & Back dealt with.
328 - 100 = 228
64 - 28 = 36
36 * 2 = 72
228 - 72 = 156
...
OR
6^3 = 216
Given the linear function f(x) 2/3x + 6 evaluate f(-6)
the answer is on the photo
Let a >= b.
show that gcd(a,b) = gcd(a-b, b)
let [tex] \gcd(a,b)= G[/tex] , $a\ge b$
$\therefore a=G\cdot m$ and $b=G\cdot n$
$a-b=Gm-Gn=G(m-n)$
Now, $\gcd(a-b,b)$ clearly is, $G$
The table shows the probability distribution of student ages in a high school
with 1500 students. What is the expected value for the age of a randomly
chosen student?
Age
13
14
15
16
17
18
Probability 0.01 0.23 0.26 0.28 0.20 0.02
Answer:
Exoected age is 15.49 years
Step-by-step explanation:
Expected age
= E(x)
= sum (p(i)*i)
= 13*0.01+14*0.23+15*0.26+16*0.28+17*0.20+18*0.02
= 15.49
Given that f(x) = x + 4 and g(x) = x + 7, find (g - 4(x).
Answer: The value of [tex](g - f)(x)=4 .[/tex]
Step-by-step explanation:
Given functions : [tex]f(x) = x + 4[/tex] and [tex]g(x) = x + 7[/tex]
To find : [tex](g - f)(x)[/tex]
Difference between two functions: [tex](u-v)(x)=u(x)-v(x)[/tex]
Then, [tex](g-f)(x)=g(x)-f(x)[/tex]
[tex]=(x+7)-(x+4)=x+7-x-4\\\\=7-4=3[/tex]
Hence, the value of [tex](g - f)(x)=4 .[/tex]
1) Sử dụng phương pháp diện tích chứng minh định lí Pitago: “Trong một tam giác vuông, bình phương cạnh huyền bằng tổng bình phương hai cạnh góc vuông”.
2) Chứng minh rằng tứ giác có một và chỉ một đường nối trung điểm hai cạnh đối chia tứ giác thành hai phần có cùng diện tích là hình thang.
Answer:
hmm i thought abt it and i think the answer is no
Step-by-step explanation:
PLEASE HELP ME!!! The students in Suzanne's school are painting a rectangular mural outside the building that will be 15 feet by 45 feet. To prepare they are create a scale drawing that represents 20% of the given dimensions. What is the length and width of the scale drawing?
Answer:
length of scale drawing = 9 feet
width of scale drawing = 3 feet
Step-by-step explanation:
Actual dimension 15 feet by 45 feet.
length = 45 feet
width = 15 feet
Dimension on drawing is 20% of actual dimension.
20% = 20/100
Thus,
20% of 15 feet = 20/100 * 15 feet = 3 feet
20% of 45 feet = 20/100 * 45 feet = 9 feet
Thus, length of scale drawing = 9 feet
width of scale drawing = 3 feet
a game is played with a fishpond containing 100 fish; 90 white, 9 red, and 1 blue. a contestant randomly catches a fish and receives payments as follows: $0.30 for white, $1.00 for red, and $10.00 for blue. If it cists $0.60 to play this game, how much (on average) does a contestant win on each play
Answer:
loses 14 cents
- $0.14
Step-by-step explanation:
90% $0.30 $(0.30) $(0.27)
9% $1.00 $0.40 $0.04
1% $10.00 $9.40 $0.09
$(0.14)
use the spinner to find the probability
Answer:
P(multiple of 5) = 0.1667
Step-by-step explanation:
The multiples of 5 on the spinner are 5 and 10. This means out of 12 numbers, only 2 multiples of 5. Therefore, there is a 2/12 chance to get a multiple of 5.
[tex]\frac{2}{12}=\frac{1}{6}=0.1667[/tex]
Therefore, P(multiple of 5) = 0.1667.
2067 Supp Q.No. 2a Find the sum of all the natural numbers between 1 and 100 which are divisible by 5. Ans: 1050
5
Answer:
1050
Step-by-step explanation:
Natural Numbers are positive whole numbers. They aren't negative, decimals, fractions. We can just divide 5 into 100 to find how many natural numbers go up to 100 and just add them but that is just to much.
There is a easier method.
E.g: Natural Numbers that are divisible by a Nth Number. is the same as adding the Nth Numbers to a multiple of that Nth Term. For example, let say we need to find numbers divisible by 2. We know that 4 is divisible by 2 because 4/2=2. We can add the Nth numbers which is 2 to 4. 4+2=6. And 6 is divisible by 2 because 6/2=3. We can call this a arithmetic series. A series which has a pattern of adding a common difference
Back to the problem, we can use the sum of arithmetic series formula,
[tex]y = x( \frac{z {}^{1} + {z}^{n} }{2} )[/tex]
Where x is the number of terms in our sequence. Z1 is the fist term of our series. ZN is our last term. And y is the sum of all of the terms
The first term is 5, the numbers of terms being added is 20 because 100/5=20. The last term is 100.
[tex]y = 20( \frac{5 + 100}{2} )[/tex]
[tex]y = 20( \frac{105}{2} )[/tex]
[tex]y = 1050[/tex]
How??????????????????????
Answer:
y=-1/3x+7
Step-by-step explanation:
y=mx+c
m=-1/3, c=7
y=-1/3x+7
Suppose that the neighboring cities of Tweed and Ledee are long-term rivals. Neal, who was born and raised in Tweed, is confident that Tweed residents are more concerned about the environment than the residents of Ledee. He knows that the average electricity consumption of Tweed households last February was 854.11 kWh and decides to test if Ledee residents used more electricity that month, on average. He collects data from 65 Ledee households and calculates the average electricity consumption to be 879.28 kWh with a standard deviation of 133.29 kWh. There are no outliers in his sample data. Neal does not know the population standard deviation nor the population distribution. He uses a one-sample t-test with a significance level of α = 0.05 to test the null hypothesis, H0:µ=854.11, against the alternative hypothesis, H1:μ>854.11 , where μ is the average electricity consumption of Ledee households last February. Neal calculates a t‑statistic of 1.522 and a P-value of 0.066.
Based on these results, complete the following sentences to state the decision and conclusion of the test.
Neal's decision is to__________ the __________ (p 0.066). There is_________ evidence to _________ the claim that the average electricity consumption of ____________ is _________ , ________
Complete Question
The option to the blank space are shown on the first uploaded image
Answer:
Neal's decision is to fail to reject the null hypothesis (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all Ledee household is greater than , 854.28 kWh
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 854.11[/tex]
The sample size is [tex]n = 65[/tex]
The sample mean is [tex]\= x = 879.28 \ kWh[/tex]
The standard deviation is [tex]\sigma = 133.29 \ kWh[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o: \mu = 854.11[/tex]
The alternative hypothesis is [tex]H_a : \mu > 854.11[/tex]
The t-statistics is [tex]t = 1.522[/tex]
The p-value is [tex]p-value = 0.066[/tex]
Now from the given data we can see that
[tex]p-value < \alpha[/tex]
Generally when this is the case , we fail to reject the null hypothesis
So
Neal's decision is to fail to reject the null hypothesis (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all Ledee household is greater than , 854.28 kWh
HELP ASAP ROCKY!!! will get branliest.
Answer:
work pictured and shown
Answer:
Last one
Step-by-step explanation:
● [ ( 3^2 × 5^0) / 4 ]^2
5^0 is 1 since any number that has a null power is equal to 1.
●[ (3^2 ×1 ) / 4 ]^2
● (9/4)^2
● 81 / 16
We have seen how to convert specified odds from a "fair bet" into the gamblerâs belief about the likelihood of an event happening. The following are related.a. Torik gives 5:3 odds that someone will walk in late for class tomorrow. What probability does lie assign for this event? b. Mikko believes there is a 60% chance that at least five students from this class will be at the next basketball game. If he were to set up odds, what would they be? c. Change the 60% to 75%. Now would would be the odds?