Answer:
0.123
Step-by-step explanation:
Use the random variable E - S, which will follow a normal distribution with a mean of 70 - 60 = 10 and SD = \sqrt{5^2+7^}
P(E - S < 0) = 0.123
The probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123.
What is the normally distributed data?Normally distributed data is the distribution of probability which is symmetric about the mean.
The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
A company advertises two car tire models. The number of thousands of miles that the standard model tires last has a mean and standard deviation,
[tex]\mu_S= 60[/tex]
[tex]\sigma_S = 5[/tex]
The number of miles that the extended life tires last has a mean and standard deviation,
[tex]\mu_E = 70[/tex]
[tex]\sigma_E = 7[/tex]
Use the E-S random variable rule,
[tex]E=\mu_E-\mu_s\\E=70-60\\E=10[/tex]
Similarly, the value of S,
[tex]E=\sqrt{\sigma^2_E+\sigma^2_s}\\S=\sqrt{7^2+5^2}\\S=\sqrt{49+25}\\S=\sqrt{74}\\S=8.60[/tex]
For this E-S value, the value of probability from the table of normal distribution, we get as 0.123.
[tex]P(E - S < 0)=0.123[/tex]
Thus, the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123.
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Gabriella and her children went into a grocery store and where they sell apples for $1 each and mangos for $0.50 each. Gabriella has $15 to spend and must buy at least 19 apples and mangos altogether. If Gabriella decided to buy 13 mangos, determine the maximum number of apples that she could buy.
Answer:
Step-by-step explanation:
Let x represent the number of apples that she wants to buy.
The grocery store sells apples for $1 each and mangos for $0.50 each.
If Gabriella decided to buy 13 mangos, it means that the cost of buying x apples and 13 mangoes is expressed as
x + 13 × 0.5 = x + 6.5
If she buy at least 19 apples, it means that
x + 13 ≥ 19
x ≥ 19 - 13
x ≥ 6
Gabriella has $15 to spend. It means that
x + 6.5 ≤ 15
x ≤ 15 - 6.5
x ≤ 8.5
Therefore, the maximum number of apples that she can buy is 8
Final answer:
After purchasing 13 mangos, Gabriella can spend the remaining $8.50 on apples, which allows her to buy a maximum of 8 apples while also meeting the minimum requirement of 19 fruits in total.
Explanation:
If Gabriella decided to buy 13 mangos at $0.50 each, she would spend $6.50 on mangos. She has $15 to spend, so after buying the mangos, she would have $15 - $6.50 = $8.50 left. Since apples cost $1 each, Gabriella could buy a maximum of $8.50/ $1 per apple = 8 apples. However, she must buy at least 19 apples and mangos altogether. Since she has already bought 13 mangos, she would need to buy 19 - 13 = 6 apples to meet the minimum requirement. Therefore, the maximum number of apples she can buy is 8, which also satisfies the minimum quantity of fruit required.
Which inequality statement describes the two numbers on a number line?
"−7 and a number 5 units to the right of −7"
A) 5 < −7
B) 5 > −7
C) −7 > −2
D) −7 < −2
Answer:
Option C)
[tex]-7<-2[/tex]
Step-by-step explanation:
We are given the following in the question:
"-7 and a number 5 units to the right of -7"
The nubmer 5 units to the right of -7 will be:
[tex]=-7 + 5\\=-2[/tex]
The number line shows the two marked points.
As observed from the number line, we can write the inequality:
[tex]-7<-2[/tex]
Thus, the correct option is
Option C)
[tex]-7<-2[/tex]
Answer:
its d not c so -7<-2 is the awnser
Mrs. Wilton is planning a rectangular flower box for her front window. She wants the flower box to hold exactly 16 cubic feet of soil.How many flower boxes with different-size bases will hold exactly 16 cubic feet of soil, using whole-number dimensions?flower boxes with different-size bases will hold exactly 16 cubic feet of soil. please no fake answers or you not getting nothing
There are 4 different flower boxes with different-size bases that can hold exactly 16 cubic feet of soil when using whole-number dimensions. These consist of dimension combinations of 1x1x16, 1x2x8, 1x4x4, and 2x2x4 feet.
Mrs. Wilton is planning a rectangular flower box that should have a volume of 16 cubic feet. To find how many flower boxes with different-size bases can hold exactly 16 cubic feet of soil, we need to find all the possible combinations of whole-number dimensions (length, width, and height) that when multiplied together equal 16 cubic feet. We must remember that volume is calculated as Length x Width x Height. Since 16 is the volume in cubic feet, we look for whole-number factors of 16.
Here are the possible whole-number dimension sets (in feet) for a volume of 16 cubic feet:
1 x 1 x 16 (Height can be 1, 16, or any factor of 16)
1 x 2 x 8 (Height can be 2, 8, or any factor of 16)
1 x 4 x 4 (Height can be 4 or any factor of 16)
2 x 2 x 4 (These dimensions are interchangeable)
Each of these dimensions gives a different base size for the flower box, and all ensure the volume is 16 cubic feet. Thus, there are 4 different flower boxes with different-size bases that will hold exactly 16 cubic feet of soil.
Jenny invests $1,599 in a retirement account with a fixed annual interest rate of 9% compounded continuously. How long will it take for the account balance to
reach $3.002.30?
o
А буеаrѕ
0
B. 7 years
0
c. 9 years
0
D. 8 years
Answer:
Step-by-step explanation:
Factor x2 – 2x – 80.
A. (x – 3)(x + 10)
B. (x + 6)(x - 1)
C. (X + 8)(x - 10)
D. (+3)(x+6)
Answer:
(x-10) (x+8)
Step-by-step explanation:
x^2 – 2x – 80.
What two numbers multiply to -80 and add to -2
-10*8 = -80
-10+8 = -2
(x-10) (x+8)
=====================================================
Explanation:
The last term is -80 and the middle coefficient is -2
Find two numbers that
Multiply to -80, and,add to -2Those two numbers are 8 and -10
8 times -10 = -808 plus -10 = -2which is why the original expression factors to (x+8)(x-10)
We can use the FOIL rule to expand out (x+8)(x-10) to end up with x^2-10x+8x-80 = x^2-2x-80, which confirms we have the correct factorization. You can use the box method as an alternative.
If you meet a person online there is a 50% chance that they aren't who they say they are. There is a 75% chance that part of what they tell you is the truth. What are the chances that they are who thy say they are.
Any help is appreciated! Question in picture.
Answer:
Step-by-step explanation:
1.65
Answer:
1.65
Step-by-step explanation:
choose $16.50 / 10 pounds = $1.65
You donate 8 baseballs to a local baseball team. Your uncle donates 12 baseballs. If a total of 50 baseballs are donated, what is the probability that the first pitch of the season uses one of your baseballs or one of your uncle’s baseballs?
The required probability that the first pitch of the season uses one of your baseballs or one of your uncle's baseballs is 2/5.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
There are 20 baseballs donated between you and your uncle and a total of 50 baseballs, so the probability that the first pitch of the season uses one of your baseballs or one of your uncle's baseballs is:
P(your baseball or uncle's baseball) = (number of your baseballs + number of uncle's baseballs) / total number of baseballs
= (8 + 12) / 50
= 20/50
= 2/5
Therefore, the probability that the first pitch of the season uses one of your baseballs or one of your uncle's baseballs is 2/5.
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The probability that the first pitch of the season uses one of the baseballs donated by the student or their uncle is 2/5 or 40%.
To calculate the probability that the first pitch of the season uses one of your baseballs or one of your uncle's, we first need to figure out the total number of baseballs donated by you and your uncle. You donated 8 baseballs and your uncle donated 12 baseballs. Hence, together you both donated 8 + 12 = 20 baseballs.
Since there are a total of 50 baseballs donated, we can now calculate the probability. The probability of picking either one of your baseballs or one of uncle's baseballs is the total number of your combined baseballs divided by the overall total number of baseballs, which is 20/50. This can be simplified to 2/5 or 40%.
Therefore, the probability that the first pitch of the season uses one of the baseballs donated by you or your uncle is 2/5.
The results of a color spinner experiment are shown in the table. Consider the experimental probability of the spinner landing
on green. If the experiment is repeated with 50 spins, what is the prediction for the number of spins that will land on green?
Frequency
Result
Blue
Red
Green
Yellow
colos
Save and Exit
Next
Submit
Mark this and return
If the experiment is repeated with 50 spins, the prediction for the number of spins that will land on green is 5
From the question, we have the following parameters that can be used in our computation:
The table of values
Calculate the total number of spins
So, we have
Total spins = 5 + 3 + 1 + 1
Total spins = 10
We have that
The frequency of landing on green is 1
The experimental probability of landing on green is then represented as
[tex]\[ \text{Probability of green} = \frac{1}{10} \][/tex]
Using the experimental probability to predict the number of spins that will land on green in 50 spins, we have
Predicted number of green spins = [tex]\frac{1}{10} \times 50 = 5[/tex]
So, if the experiment is repeated with 50 spins, the prediction for the number of spins that will land on green is 5
Question
The results of a color spinner experiment are shown in the table. Consider the experimental probability of the spinner landing
on green. If the experiment is repeated with 50 spins, what is the prediction for the number of spins that will land on green?
Result Frequency
Blue 5
Red 3
Green 1
Yellow 1
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C (x) = 0.5x^2-130x+17,555. What is the minimum unit cost?
The minimum unit cost to manufacture a car for the given quadratic cost function C(x) = 0.5x^2 - 130x + 17,555 is found by using the vertex formula. The x-coordinate of the vertex is -(-130)/(2*0.5) = 130, which yields the minimum unit cost of $9,105 when substituted back into the function.
Explanation:To find the minimum unit cost for manufacturing cars in the given scenario, we need to analyze the cost function C(x) = 0.5x2 - 130x + 17,555. This is a quadratic function, which is parabolic in shape, generally either opening upwards or downwards. In this case, we have a positive coefficient for the x2 term, which means the parabola opens upwards and the vertex of this parabola will give us the minimum point or the minimum cost for producing cars.
The vertex of a quadratic function expressed in the form ax2 + bx + c can be found using the formula -b/(2a) for the x-coordinate of the vertex. In this case, a = 0.5, b = -130, so the x-coordinate of the vertex is -(-130)/(2*0.5) = 130. Plugging this value into the original function will give us the minimum unit cost C(130).
The calculation is as follows:
C(130) = 0.5 * (130)2 - 130 * (130) + 17,555
C(130) = 0.5 * 16,900 - 16,900 + 17,555
C(130) = 8,450 - 16,900 + 17,555
C(130) = 9,105
Therefore, the minimum unit cost to manufacture a car in this scenario is $9,105.
does x^2-6x+3 have solutions that are real numbers
Answer:
X=10.8 and X=1.1
Step-by-step explanation:
Δ= b^2-4ac
= (-6)^2-4(1)(3)
=24
X1=
[tex] \frac{6 + \sqrt{24} }{ {1}^{2} } [/tex]
=10.8
X2=
[tex] \frac{6 - \sqrt{4} }{ {1}^{2} } [/tex]
=1.1
geometry please help
Answer:
b. 46°
Step-by-step explanation:
In a circle, measure of minor arc is equal to the measure of its corresponding central angle.
[tex] \therefore m\overset{\frown} {BD} = m\angle BAD = 148°\\
\because m\overset{\frown} {BD}= m\overset{\frown} {BC}+ m\overset{\frown} {CD}\\
\therefore 148° = 102° + m\overset{\frown} {CD}\\
\therefore m\overset{\frown} {CD}= 148° - 102°\\
\huge\purple {\boxed {\therefore m\overset{\frown} {CD}= 46°}} \\ [/tex]
The expression 62.4d-21062.4d−21062, point, 4, d, minus, 210 gives the number of Indian rupees you receive when you exchange \$d$ddollar sign, d at the local currency exchange
Answer:601.2
Step-by-step explanation:
A game increased in price by 1/2.. After the increase it was priced at £27. What was the original price of the game? I am very confused (hegarty maths)
The original price of the game was £18. This is derived by understanding a 1/2 increase equates to a 50% increase, thus making £27 150% of the original price. To get the original price, divide £27 by 1.5.
Explanation:To solve this problem, you need to understand that an increase of 1/2 equals a 50% increase. If the game price were £27 after increasing by 50%, that means £27 represents the original price plus an additional half (50%) of the original price, in other words, it represents 150% of the original price. We can set up the equation like this:
Original Price(1.5) = £27
To solve for the original price, we divide £27 by 1.5, resulting in £18.
So, the original price of the game was £18.
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Jami is keeping track of the weather for a class project she recorded data on 16 days out of 16 days 1/4 were clear blue skies how many days had clear blue skies
Answer:
4 days
Step-by-step explanation:
She recorded date for 16 days, and 1/4 of the days were clear blue skies.
One way to find this is to multiply 16 and 1/4
16*1/4=4
Another way is to first convert 1/4 to a decimal
1/4=0.25
Then multiply 16 and 0.25
16*0.25 =4
So, 4 out of 16 days had clear blue skies
ASAP show work please
Answer:
20 degrees
Step-by-step explanation:
Because lines CB and DA cross in the center of the circle, they are vertical angles and they are equidistant from arcs AB and CD. This means that CD and AB are congruent, and that therefore CD=AB=20 degrees. Hope this helps!
Find the point, M, that divides segment AB into a ratio of 2:1 if A is at (-1, 2) and B is at (8, 15). A) (6, 8) B) (6, 26 3 ) C) (5, 32 3 ) D) (5, 26 3 ) 27)
Answer:
Hence, the coordinate of point M that divides the line segment AB is [tex](5, \frac{32}{3} )[/tex].
Step-by-step explanation:
Given that,
AB is the line segment, and M divides the line segment AB into a ratio of 2:1.
Coordinate of point A is [tex](-1, 2)[/tex] and Coordinate of point B is [tex](8, 15)[/tex].
Let, the coordinate of point M is [tex](x. y)[/tex].
Now,
The coordinate of a point M, which divides the line segment AB internally in the ratio [tex]m_{1}:m_{2}[/tex] are given by:
[tex]\frac{m_{1}x_{2}+m_{2}x_{1} }{(m_{1}+m_{2}) } ,\frac{m_{1}y_{2}+m_{2}y_{1} }{(m_{1}+m_{2}) }[/tex]
[tex]x[/tex] coordinate of point M is [tex]\frac{(2\times 8)+(1\times -1)}{(2+1)}[/tex] = [tex]\frac{(16-1)}{3} =\frac{15}{3} =5[/tex]
[tex]y[/tex] coordinate of point M is [tex]\frac{(2\times 15)+(1\times 2)}{(2+1)}[/tex] = [tex]\frac{30+2}{3} = \frac{32}{3}[/tex]
Hence, the coordinate of point M that divides the line segment AB is [tex](5, \frac{32}{3} )[/tex].
what is the answer for x+5=15
Answer:
x=10
Step-by-step explanation:
Answer:
x=10
Step-by-step explanation:
x+5=15
-5=-5
---------------
x= 10
A drawer contains 5 black socks(B), 7 grey socks(G) and 13 white socks(W). Matthew selects two socks from the drawer at random. What is the probability that they are the same color? Give your answer as a decimal correct to three significant figures.
Answer:
0.363
Step-by-step explanation:
Number of Black(B) Socks =5
Number of Grey(G) Socks =7
Number of White(W) Socks =13
Total Number of Socks=5+7+13=25
If the two socks are picked one after the other, the total number reduces and the number of that particular color of socks picked also reduces.
To pick the same color, they could either be both black, grey of white.
Therefore:
P(they are of the same color)=P(BB)+P(GG)+P(WW)
[tex]=(\frac{5}{25}X\frac{4}{24})+(\frac{7}{25}X\frac{6}{24})+(\frac{13}{25}X\frac{12}{24})\\=0.363[/tex]
The probability that they are of the same color is 0.363 correct to 3 significant figures.
Determine which of the following graphs does not represent a function.
(Help me ASAP)
Answer:
D
Step-by-step explanation:
one way to determine whether or not something is a function is to use the vertical line test
You can draw vertical lines all along the figure and if the same vertical line touches 2 parts of the graph we know this is not a function due to there being 2 outputs for the same x value
d is a vertical line and therefore will not pass this test
can someone help me with this geometry plz??? will mark brainliest and 20 points!!
Answer:
A unique
Step-by-step explanation:
2 triangles are similar if they have the same angle measures, by the law of triangle similarity.
That means that given 2 angles measures, we can find our third angle measure and create infinitely many triangles with those 3 angles. however we have a given side length. changing the length of this will not satisfy the given conditions
One circle is 1962.5ft.It’s 32 circles. So how many ft is that ?
I’m not sure of what to do ,can u please help me ?
Please I’ve been stuck on this for hours.
Answer:
Out of 240,000 feet² of the field 62,800 feet² was being watered.
Step-by-step explanation:
We have a figure with 32 circles and diameter of each circle is 50 feet. We have to find how much area is being watered. Assuming that each circle represents the Area of the field which is being watered.
We can find the area of one circle and multiply that by 32 to find the area of all 32 circles. This will give us the area of the field that is being watered.
Since, radius is half of the diameter, the radius of each circle will be r = 25 feet.
Area of a circle is calculated as:
Area = πr²
Substituting the value of r = 25 and π = 3.14, we get:
Area of one circle = 3.14 x (25)² = 1962.5 feet²
Since area of 1 circle is 1962.5 feet² , area of 32 circles will be = 32 x 1962.5 = 62,800 feet²
The field is rectangular in shape with length = 600 feet and width = 400 feet.
Area of a rectangle is the product of its length and width. So area of the entire field will be:
Area of field = 600 x 400 = 240,000 feet²
This means, out of 240,000 feet² of the field 62,800 feet² was being watered.
What are the zeros of this function?
Answer:
Answer:
X=3 and X=6
Step-by-step explanation:
When y is zero
Step-by-step explanation:
Answer:
Its b
Step-by-step explanation:
The data plot represents the hours student each week in two different classrooms
Answer:
Could you put a link or image or pic
Step-by-step explanation:
We can not see
Answer:
the mean number of hours a student in Mr. Hart’s class studies is hours 4.6
The mean number of hours a student in Ms. Perry’s class studies is 2.8 hrs
A typical student in Mr. Hart’s class studies a typical student in Ms. Perry’s class.more than
Step-by-step explanation:
just took the test
Jiffy Mix in Chelsea, Michigan has a machine that fills the Jiffy Corn Muffin Mix boxes with Mix. It dispenses corn muffin mix with a normal distribution and has a mean of 10.0 and a standard deviation of 0.1 ounces
Question:
A. The middle 95% of Jiffy Corn Muffin Mix boxes contain between _____ and ________ounces of cereal
Answer:
Therefore the middle 95% of Jiffy Corn Muffin Mix boxes contain between _9.994____ and _10.0062_______ounces of cereal
Step-by-step explanation:
The question requires us to construct the 95% confidence interval of the normal distribution as follows;
The mean, μ = 10
The sample standard deviation, σ = 0.1
Assumption
Number of boxes, n = 1000
The formula for confidence interval is as follows;
[tex]CI= \mu \pm z\frac{\sigma}{\sqrt{n}}[/tex]
Where, z at 95% confidence level is given as ±1.96
Plugging in the values, we have;
[tex]CI=10 \pm 1.96 \times \frac{0.1}{\sqrt{1000}}[/tex]
Therefore the middle 95% of Jiffy Corn Muffin Mix boxes contain between _9.994____ and _10.0062_______ounces of cereal.
Between x=2 and x=3 which function has a greater average rate of change than y=1/3^-x
A)y=2^x
B)y=5^x-2
C)y=1/4^-x
D)y=2/3^-x
Answer:
C) y = (1/4)^(-x)
Step-by-step explanation:
The average rate of change on an interval [a, b] is found using the formula ...
arc = (f(b) -f(a))/(b -a)
For an exponential function with base b on interval [2, 3], the rate of change is ...
arc = (b^3 -b^2)/(3 -2) = b^2(b -1)
This expression assumes a positive sign on the exponent.
We can compute the arc for each answer choice as ...
(reference) 1/3^-x = 3^x ⇒ arc = 3²(3 -1) = 18
A) 2^x ⇒ arc = 2²(2 -1) = 4
B) 5^(x-2) = (1/25)5^x ⇒ arc = (1/25)(5²)(5 -1) = 4
C) 1/4^-x = 4^x ⇒ arc = 4²(4 -1) = 48
D) (2/3)^-x = (3/2)^x ⇒ arc = (3/2)²(3/2 -1) = 9/8
An average rate of change greater than 18 is demonstrated by (1/4)^-x.
Write the number 54300 in standard form
Answer:
5.4300 x 10 with a small 4
Step-by-step explanation:
Answer:
5.43*10^4
Step-by-step explanation:
The mean age of five children is 8 years
4 months. When Amina joins the children,
their mean age becomes 8 years 5 months.
How old is Amina?
Answer:
9
Step-by-step explanation:
Answer:
its 8
Step-by-step explanation:
Simplify the following expression.
7(2y + 5z) - 35z
A.
9y
B.
14y - 40z
C.
9y - 70z
D.
14y
Answer: 14y
Step-by-step explanation:
7 times 2 = 14
7 times 5 = 35
14y + 35z - 35z
35 - 35 = 0
You are left with 14y
On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The locust population increases by a factor of 555 every 222222 days, and can be modeled by a function, LLL, which depends on the amount of time, ttt (in days). Before the first day of spring, there were 760076007600 locusts in the population. Write a function that models the locust population ttt days since the first day of spring.
Answer: L(t)= 7600 times 5^t/22
Step-by-step explanation:
kahn answer
To model the locust population, we can use an exponential growth function. The initial population is given as 7600, and it increases by a factor of 555 every 222222 days. The function is L(t) = 7600 * 555^(t/222222).
Explanation:To model the locust population, we can use an exponential growth function. The initial population is given as 7600. The population increases by a factor of 555 every 222222 days. Let's denote the time since the first day of spring as t. The function can be written as:
L(t) = 7600 * 555^(t/222222)
For example, if we want to find the locust population after 1 year (365 days), we can substitute t = 365 into the function:
L(365) = 7600 * 555^(365/222222)
By evaluating this expression, we can determine the locust population at any given time since the first day of spring.