Answer:
0.025
Step-by-step explanation:
-This is a conditional probability problem.
-Let L denote lens defect and C charging defect.
#We first calculate the probability of a camera having a lens defect;
[tex]P(lens)=\frac{Lens}{Total}\\\\=\frac{20}{800}\\\\=0.025[/tex]
#Calculate the probability of a camera having a charging defect:
[tex]P(Charging)=\frac{Charging}{Total}\\\\=\frac{25}{800}\\\\=0.03125[/tex]
The the probability that a camera has a lens defect given that it has a charging defect is calculated as:
[tex]P(L|C)=\frac{P(C)P(L)}{P(C)}\\\\=\frac{0.025\times 0.03125}{0.03125}\\\\=0.025[/tex]
Hence, the probability that a camera has a lens defect given that it has a charging defect is 0.025
The probability that a camera has a lens defect given that it has a charging defect is 6/25 or 0.24.
The question asks for the probability that a camera has a lens defect given that it has a charging defect. To find this probability, we use the concept of conditional probability. From the data given, 25 cameras have charging defects and 6 cameras have both defects. The probability that a camera has both a lens and charging defect among those with a charging defect is:
P(Lens defect | Charging defect) = P(Lens and Charging defect) / P(Charging defect)
Which translates to:
P(Lens defect | Charging defect) = Number of cameras with both defects / Number of cameras with charging defects
P(Lens defect | Charging defect) = 6 / 25
Therefore, the probability is 6/25 or 0.24.
Bryant’s pool contains 13,000 gallons of water.
The maximum rate at which the city allows pools to be drained is 720 gallons per hour.
Write a function that represents the number of gallons of water left in Bryant’s pool t hours after he starts draining, if he drains the pool at the maximum rate.
Answer:
13000=t720
Step-by-step explanation:
720 x t = 13000
The function that represents the number of gallons of water left in Bryant’s pool t hours after he starts draining is 13,000 - 720t.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given Bryant’s pool contains 13,000 gallons of water. The maximum rate at which the city allows pools to be drained is 720 gallons per hour. Therefore, the equation can be written as,
Water left = 13,000 - 720t
Hence, the function that represents the number of gallons of water left in Bryant’s pool t hours after he starts draining is 13,000 - 720t.
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Multiply (3)(−4)(2) what is the answer i need it really quick thx
Answer:
-24
Step-by-step explanation:
First multiply 4 and 3. You can just add the negative after you multiply.
Use simple multiplication facts. So
4 x 3=12
So it will be -12
Then, do the same, but with 12 and 2.
12 x 2=24
So it will be -24
Final answer:
-24
What is the next term of the geometric sequence?
2,−10,50,...
Answer:
-250
Step-by-step explanation:
I don't know for sure but I hope it's correct.
Answer:
-250
Step-by-step explanation:
Can someone please help me?
Bella plans to put 200 into her savings account. She can place her money into an account represented by p(x)=3x+200 or into another account represented by n(x)=200(1.04)x which account has the highest value in 4 years? Which account has the highest in 15 years?
Answer:
It’s c
Step-by-step explanation:
Find a number which decreased by 24 equals 3 times it’s opposite
x - 24 = 3 (-1) x
x - 24 = -3x
-24 = -4x
x = 6
Step-by-step explanation:
The number which decreased by 24 equals 3 times its opposite is 6
Finding the number which decreased by 24 equals 3 timesLet x represent the number to calculate
The opposite of the number is -x.
According to the problem, we have the following equation:
x - 24 = 3(-x)
Simplifying the equation:
x - 24 = -3x
Adding 3x to both sides:
4x - 24 = 0
Adding 24 to both sides:
4x = 24
Dividing both sides by 4:
x = 6
Hence, the number is 6.
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For which value of 0 is sin 0= -1
Answer:
3/2 π
Step-by-step explanation:
If you realize that the sin is actually the y coordinate of a (unit) circle when you travel around it, you will know that it is -1 when you are 3 quarters round, assuming you started at (1,0).
The circumference is measured in radians, where one round is 2π.
So 3/4 of 2π is 3/2 π.
In degrees, the answer is 3/4 of 360°, which is 270°.
Hope that was helpful.Thank you!!!
Answer:
Step-by-step explanation:
I will mark brainliest !!!! ANSWER PART B PLEASE (:
Answer:
The selling price of the remote control car is $36.3
Step-by-step explanation:
In this question, we are tasked with calculating the selling price of the remote control car.
From the first part of the question, we were made to know that he applies a markup of 21% and luckily for us, we are told that the expression for the retail price given the markup is 1.21 c
This means 1.21 × the cost price of the remote car
Hence, to calculate the selling price, we simply substitute $30.00 for the value of c.
The selling price is thus 1.21(30) = $36.3
The length of a rectangle is 8 inches longer than half of its width.The area of the rectangle is 18 square inches.How many inches wide is the rectangle
Answer:
The correct answer is 2 inches.
Step-by-step explanation:
Let l inches and w inches be the length and width of a rectangle respectively.
According to the given problem, l - 8 = [tex]\frac{w}{2}[/tex].
Area of the rectangle is given to be, according to the question, 18 square inches.
Thus l × w = 18
⇒ l × (2l - 16) = 18
⇒ 2 [tex]l^{2}[/tex] - 16l - 18 = 0
⇒ [tex]l^{2}[/tex] - 8l - 9 = 0
⇒ ( l - 9) ( l + 1) = 0
The possible values of l are 9 and -1. As the length cannot be equal to -1, thus the value of the length is 9 inches.
Width of the rectangle is 2 inches.
You open up a new case of note cards packs for your office. Each pack contains 50 note cards and each case contains 20 packs. If you were to evenly divide up the note cards between you and your 9 co-workers, how many note cards will each person receive?
1 case of note cards = 20 packs
1 pack = 50 note cards
50 x 20 = 1000 note cards in one case.
1000 / 10 = 100
Each person will receive 100 note cards.
Hope this helps!! :)
Leah has a 22 ounce coffee. She drinks 7 ounces. Enter the percentage of ounces Leah has
left of her coffee. Round your answer to the nearest hundredth.
Answer:
The coffee Leah has left in percentage is 68.18%
Step-by-step explanation:
Given data
Total available coffee = 22 ounces
Amount She took out = 7 ounces
Let us carry out a simple subtraction arithmetic to find out the remainder
Hence remaining coffee = 22-7= 15
To expressing the remainder as a percentage we have
(15/22)*100=0.6818*100
= 68.1818%
To the nearest hundredths we have
= 68.18%
Answer: 68.18%
Step-by-step explanation:
Leah has a 22 ounce coffee and she drinks 7 ounces of the coffee. This means she will have:
22 - 7 = 15 ounces left.
The percentage of ounces of coffee Leah has left of her coffee will be the number of ounces left divided by the total number of ounces of coffee multiplied by 100. This will be:
= 15/22 × 100
= 0.6818 × 100
= 68.18%
The percentage of coffee Leah has left is 68.18%.
The sun casts a 70 foot shadow on a 30 foot tree. Find the angle of elevation to the nearest degree.
Answer:
23°
Step-by-step explanation:
We apply Pythagorean theorem to determine the missing length, Hypotenuse:
[tex]h^2+b^2=H^2\\\\70^2+30^2=H^2\\\\H=\sqrt{5800}\\\\=76.15773\ ft[/tex]
This hypotenuse corresponds to the right triangle and the tree's height, corresponds to the angle of elevation:
-We apply the law of Sines;
[tex]\frac{a}{Sin \ A}=\frac{b}{Sin\ B}\\\\\\\frac{76.15773}{Sin \ 90}=\frac{30}{Sin\ h}\\\\h=Sin^{-1}\frac{30}{76.15773}\\\\=23.19859\approx 23\textdegree[/tex]
Hence, the angle of elevation is 23°
- A right triangle has a hypotenuse of 5 feet. One leg measures one foot
less than the hypotenuse. What are both legs' measures?
Question 3 (1 point)
.
2x - 3(x + 6) = -3(x - 2)
x =
Answer:
x=12
Step-by-step explanation:
2x - 3(x + 6) = -3(x - 2)
Distribute
2x -3x -18 = -3x +6
Combine like terms
-x -18 = -3x+6
Add 3x from each side
-x+3x -18 = -3x+3x +6
2x -18 = 6
Add 18 to each side
2x-18+18 = 6+18
2x = 24
Divide each side by 2
2x/2 = 24/2
x = 12
Answer:
[tex]x = 12[/tex]
Step-by-step explanation:
[tex]2x - 3(x + 6) = - 3(x - 2) \\ 2x - 3x - 18 = - 3x + 6 \\ 2x - 3x + 3x = 18 + 6 \\ 2x = 24 \\ \\ x = \frac{24}{2} \\ \\ x = 12[/tex]
Choose a true statement
Answer:
A true statement
Step-by-step explanation:
WHAT R THE STATEMENTS
Complete the equivalent equation for -7x-60 =x^2 +10x
Answer:
(x+12)(x+5)
Step-by-step explanation:
Formula use: a²+bx+c
Make one side equal to zero:Original:
-7x-60 =x² +10x
New:
x² + 17x + 60
Multiply A with CNew:
(1)x x 60 = 60
Find factors of 60 that when added, equal to 17.New:
10 × 6, 60 × 1, 20 × 3, 5 × 12, 4 × 15
5 times 12 equal 60, but when added equal to 17.
Replace the 17 with 5 and 12New:
x² + 5x + 12x + 60
Break them off into two equationsNew:
x² + 5x l 12x + 60
Divide each equation into it's simpilest form. Make sure the numbers in the ( ) are the same.New:
x(x + 5) l +12(x+5)
Answer: (x+12)(x+5)callie has $24.65 to spend on groceries.after buying 6 potaos ,she had $18.95 left. if each potato coast the same amount,what is the price of one potato
Answer:
$5.75
Step-by-step explanation:
Find the missing values in each ratio table. Then write the equivalent ratio
Answer:
Dolls: 4,8,12
Balls: 6,12,18
Step-by-step explanation:
The completed ratio table is:
Dolls 4 4 12
Balls 6 12 6
Equivalent ratios: Dolls 1:3, Balls 1:2.
To find the missing values in the ratio table, we can set up proportions using the given ratios:
For Dolls:
4 dolls correspond to 12 dolls, so the missing value can be found using the proportion:
[tex]\(\frac{4}{12} = \frac{x}{12}\)[/tex]
[tex]\(x = \frac{4 \times 12}{12}\)[/tex]
x = 4
For Balls:
6 balls correspond to 12 balls, so the missing value can be found using the proportion:
[tex]\(\frac{6}{12} = \frac{y}{12}\)[/tex]
[tex]\(y = \frac{6 \times 12}{12}\)[/tex]
y = 6
The completed ratio table is:
Dolls 4 4 12
Balls 6 12 6
Equivalent ratio for Dolls:
[tex]\(\frac{4}{12} = \frac{1}{3}\)[/tex]
Equivalent ratio for Balls:
[tex]\(\frac{6}{12} = \frac{1}{2}\)[/tex]
A plumber needs to transport a 12 foot pipe to a jobsite. The interior of his van is 90 inches in length, 40 inches in width and 40 inches in height. Will the pipe fit inside his van?
Answer:
No
Step-by-step explanation:
First, convert all dimensions to be uniform.
1ft=0.08333 ft
90ft=90*0.0833=7.5ft
40 ft=40*0.0833=3.33 ft
The diagonal of the vehicle will be
[tex]\sqrt 7.5^{2}+3.33^{2}=8.20738150149675\ approx 8.2 ft[/tex]
Since the diagonal of vehicle is smaller than 12 ft, the pipe can't fit unless divided into two equal parts.
Final answer:
The 12-foot pipe can fit inside the van due to its dimensions.
Explanation:
The pipe is 12 feet long, which is equivalent to 144 inches. The interior dimensions of the van are 90 inches in length, which is shorter than the length of the pipe,
40 inches in width, and 40 inches in height, providing enough width and height for the pipe to fit. Therefore, the pipe will fit inside the plumber's van comfortably.
how to find the area of a complex shape
Answer:
B. 114 cm²
Step-by-step explanation:
You want to know the area of a complex shape consisting of a triangle and a semicircle.
Areas of PartsThe shape can be divided at the dotted line into two shapes whose areas you have formulas for:
semicircle of radius 5 cmtriangle with base 15 cm and height 10 cmUsing the formulas for their areas, we find the area of each shape to be ...
A = (1/2)πr² . . . . . . area of semicircle with radius r
A = (1/2)π(5 cm)² = 25/2π cm² ≈ 39 cm²
A = (1/2)bh . . . . . . area of triangle with base b and height h
A = (1/2)(15 cm)(10 cm) = 75 cm²
Total areaThe sum of the areas of the parts is ...
total area = semicircle area + triangle area
total area = 39 cm² +75 cm²
total area = 114 cm²
The area of the complex shape is about 114 cm².
What kind of slope does the following line have?
+
Answer:
horizontal and vertical
Step-by-step explanation:
if its the plus?
If Tyler’s height is 57 inches. what could be his height in centimeters
1 inch = 2.54 centimeters
Multiply.
57 * 2.54 = 144.78
Therefore, Tylers height is 144.78 centimeters.
Best of Luck!
Just before a referendum on a school budget, a local newspaper polls 354 voters to predict whether the budget will pass. Suppose the budget has the support of 55% of the voters. What is the probability that the newspaper's sample will lead it to predict defeat?
Answer:
3.07% probability that the newspaper's sample will lead it to predict defeat
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For a proportion p with n voters, we use [tex]\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}}[/tex]
In this problem, we have that:
[tex]p = 0.55, n = 354[/tex]
So
[tex]\mu = 0.55, \sigma = \sqrt{\frac{0.55*0.45}{345}}} = 0.0268[/tex]
What is the probability that the newspaper's sample will lead it to predict defeat?
That is, a percentage of 50% or less, which is the pvalue of Z when X = 0.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.5 - 0.55}{0.0268}[/tex]
[tex]Z = -1.87[/tex]
[tex]Z = -1.87[/tex] has a pvalue of 0.0307.
3.07% probability that the newspaper's sample will lead it to predict defeat
Joe wants to rent an apartment with an initial monthly rent of $1,400. He has been told that the landlord raises the rent 1.25% each year. Using an exponential function ( or a method of your own) to model this situation, calculate the rent that Joe will have to pay for the 4th year of living in the apartment.
Answer: his pay for the 4th year is $1453.16
Step-by-step explanation:
The landlord raises the rent 1.25% each year. It means that the rent is increasing in geometric progression.
The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
From the information given,
a = $1,400
r = 1 + 1.25/100 = 1.0125
n = 4 years
The 4th term(year), T4 is
T4 = 1400 × 1.0125^(4 - 1)
T4 = 1400 × 1.0125^3
T4 = $1453.16
Using an exponential function, the rent Joe will have to pay for the fourth year, with a 1.25% annual increase, is approximately $1,453.38.
To calculate the rent Joe will have to pay for the fourth year of living in the apartment with an annual rent increase of 1.25%, we will use an exponential function. The general formula for compounded growth is given by:
Future Value = Present Value ×(1 + rate)number of periods
In Joe's case, the Present Value is the initial monthly rent of $1,400, the rate is 1.25% or 0.0125 when expressed as a decimal, and the number of periods is 3 years since we are calculating the rent at the start of the fourth year. Plugging these values into the formula:
Rent for the fourth year = $1,400 × (1 + 0.0125)3
Let's calculate that:
Rent for the fourth year = $1,400 × (1.0125)3
Rent for the fourth year approximately = $1,400 × 1.038128
$1,453.38
Hence, Joe will have to pay about $1,453.38 for the fourth year of rent.
The volume of a right circular cone that has a height of 13 m and a base with a diameter of 3.4 m. Round your answer to the nearest tenth of a cubic meter.
Answer:39.3
Step-by-step explanation:
The volume of a right circular cone that has a height of 13 m and a base with a diameter of 3.4 m is 39.3 m^3
How to find volume of a right circular cone?Suppose that the radius of considered right circular cone be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
Right circular cone is the cone where the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
Given that right circular cone that has a height of 13 m and a base with a diameter of 3.4 m.
Volume can be calculated as;
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
V = 22/7×3.4×3.4×13×3.4/ 24
V = 39.3 m^3
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The cylinder shown has a radius of 3 inches. The height is three times the radius. Find the volume of the cylinder. Round your solution to the nearest tenth
Answer:
254.5 Inches Cubed
Step-by-step explanation:
Formula for Finding the Volume of a Cylinder: [tex]V=\pi r^2h[/tex]
The radius is 3 inches.
[tex]r=3[/tex]
The height is three times the radius.
Multiply the radius by three to get the height.
[tex]h=3*3\\h=9[/tex]
The height is 9 inches.
Use the formula to find the volume.
[tex]\pi (3)^29= \pi (9)9=81\pi[/tex]
The exact volume is 81[tex]\pi[/tex] inches cubed.
[tex]81 * \pi[/tex] ≈ 254.47
254.47 ≈ 254.5
The volume of the cylinder should be about 254.5 inches cubed.
Jamie and Saorise are planning a trip to Europe.
They are planning to spend 124 days on holidays, and 31 of them will be in England.
What percentage of their holiday will be spent in England?
Answer:
25%
Step-by-step explanation:
Leah and her children went into a bakery and will buy cupcakes and brownies. Each cupcake costs $4.75 and each brownie costs $3. Leah has a total of $65 to spend on cupcakes and brownies. Write an inequality that would represent the possible values for the number of cupcakes purchased, cc, and the number of brownies purchased, b.B.
Answer:
Step-by-step explanation:
C=Cupcakes
B=Brownies
$4.75 per cupcake...(4.75c)
$3.00 per brownies..(3b)
Leah has $65 only. ([tex]\leq[/tex] 65)
4.75c + 3b[tex]\leq[/tex] 65
Write The decimal as a percent .065
Answer:
6.5
Step-by-step explanation:
Which method listed below could not be used to prove that two triangles are congruent? a. Prove all three sets of corresponding sides congruent b. Prove all three sets of corresponding angles congruent c. Prove that two sides and an included angle of one triangle are congruent to two sides and an included angle of the other triangle d. Prove that two angles and an included side of one triangle are congruent to two angles\e of the other triangle.
Answer:
All corresponding sides and angles will be congruent
Step-by-step explanation:
To prove two triangles are congruent, we can use SSS, SAS, ASA, and AAS method.
Prove all three sets of corresponding angles congruent is not method of to prove two triangles are congruent.
The SSS rule states that , If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.The SAS rule states that If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruentThe ASA rule states that If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.The AAS rule states that , If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.Learn more:
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