Answer:
r = 0
Step-by-step explanation:
the first thing you can do to solve this equation is to remove the parenthesis
2r + 4 = r + 4
now subtract 4 from both sides
2r = r
subtract 4 from both sides
r = 0
that is your answer
What Interest Rate Compounded Daily (365 Days/Year) Is Required For A $23,000 Investment To Grow To $35,500 In 6 Years?
The required Interest Rate Compounded Daily (365 Days/Year) is 7.227%.
What is compound interest?Interest on interest, or compound interest, is the adding of interest to the principle sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out, so that interest is received on the principal plus previously collected interest in the next quarter.,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
where A is the final amount
P is the principal amount
r is the rate of interest
n is the number of times interest is charged in a year
t is the number of years
Given that interest Rate Compounded Daily (365 Days/Year) is required for a $23,000 Investment to grow To $35,500 In 6 Years. Therefore, we can write,
[tex]A = P(1+\dfrac rn)^{n \times t}[/tex]
[tex]35,500 = 23,000(1+\dfrac{r}{365})^{365 \times 6}\\\\\dfrac{35,500}{23,000} = (1+\dfrac{r}{365})^{2190}\\\\1.543478 = (1+\dfrac{r}{365})^{2190}\\\\1.000198 = 1+\dfrac{r}{365}\\\\\dfrac{r}{365} = 1.000198 - 1\\\\\dfrac{r}{365} = 0.000198[/tex]
r = 1.000198 x 365
r = 0.07227
r = 7.227%
Hence, the required Interest Rate Compounded Daily (365 Days/Year) is 7.227%.
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There are 8 red marbles and 6 blue marbles in a bag.
(a) What is the ratio of blue marbles to red marbles?
(b) What is the ratio of all marbles in the bag to blue marbles?
the ratio of blue marvel is 4/3
the ratio of Al marbles to blue is 7/3
You pick a card at random from an ordinary deck of 52 cards. If the card is a diamond, you get some points; if not, you lose 2 points. What value for the diamonds would make the game fair?12624 3.
Using the probability formula, the number of diamonds needed to make the game fair is determined by option (B) 6.
What is probability?Assume that there are a finite number of elementary events that are all equally likely to occur in the sample space of the experiment under consideration.
So let's say we want to determine the likelihood of an occurrence E.
So, the value of diamonds has to be:
The expected number of points that one can lose should equal the expected number of points that one can acquire for the game to be fair.
So, in order for the game to be fair, we need:
Expected points earned by selecting a diamond minus anticipated points lost by selecting a diamond.
If we choose a diamond, let's say we obtain P points.
Let X represent the random variable that records the player's score for each individual draw.
13/52 = 1/4 is the probability of selecting a diamond from a deck of 52 cards.
This is due to the fact that there are only 13 ways to choose a diamond out of the total 52 ways to choose a card.
So, the likelihood of receiving P points is 1/4, or 0.25.
The odds of not getting a diamond equal 1 minus the odds of getting a diamond equal 1 minus 0.25, which equals 0.75.
The points we receive when we don't acquire a diamond are -2. (negative since we actually lose it, so we can take it as a negative gain).
E(X) = expectation of X = 0 is therefore required (since the negative points of loosing would equate to positive point of winning, thus, making the expected overall score 0, thus, keeping it a fair game.)
We now have:
When choosing a non-diamond card, P(X = -2) equals 0.75; when choosing a diamond card, P(X = p) equals 0.25.
There are only possible values for X.
The result is:
E(X) = -2*p(X=-2)+p*p(X=p)
E(X) = -2*0.75+p*0.25
0=-1.5+0.25p
p = 1.5/0.25 = 6
Therefore, using the probability formula, the number of diamonds needed to make the game fair is determined by option (B) 6.
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Complete question:
You pick a card at random from an ordinary deck of 52 cards. If the card is a diamond, you get some points; if not, you lose 2 points. What value for the diamonds would make the game fair?
a) 12
b) 6
c) 24
d) 3
Answer:
B-6
Step-by-step explanation:
its making me type something here but question in the pic thanks :)
The value of the definite integral is 10 after breaking the limits of the integral.
What is integration?It is defined as the mathematical approach to calculating the smaller parts or components.
It is given that:
The piecewise function is given:
[tex]\rm \int\limits^4_0 {x} \, dx = \int\limits^2_0 {2} \, dx +\int\limits^4_2 {x} \, dx[/tex]
[tex]\rm \int\limits^4_0 {x} \, dx = x^2|^2_0+(1/2)x^2|^4_2[/tex]
= 4 + (1/2)[16 - 4)
= 4 + 6
= 10
Thus, the value of the definite integral is 10 after breaking the limits of the integral.
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a surveyor took some measurements of a piece of land. the owner needs to know the area of the land to determine the value. what is the area of the piece of land?
The area of the piece of land is 849 ft².
The area of the piece of land
=22 x 30 x [tex]\frac{1}{2}[/tex] x 2 + (30-12) x 21 x [tex]\frac{1}{2}[/tex]
=660 + 18 × 21×[tex]\frac{1}{2}[/tex]
=660 + 189
=849 ft²
The area is the amount that expresses the volume of a place on the plane or on a curved surface. The location of an aircraft region or aircraft place refers back to the area of a shape or planar lamina, at the same time as floor region refers to the location of an open floor or the boundary of a three-dimensional object. the area may be understood as the amount of fabric with a given thickness that could be essential to style a model of the shape, or the amount of paint vital to cowl the surface with a single coat. it's miles the 2-dimensional analog of the length of a curve (a one-dimensional concept) or the extent of a strong (a three-dimensional concept).
The place of a shape can be measured by way of evaluating the form to squares of a hard and fast size. inside the global gadget of devices (SI), the usual unit of the vicinity is the rectangular meter (written as m²), that's the location of a rectangle whose sides are one meter long. A shape with a place of three rectangular meters would have the equal region as 3 such squares. In mathematics, the unit square is described to have placed one, and the location of another shape or floor is a dimensionless real variety.
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Of the 465 sophomores at Eastside High School, exactly 13 are taking French II or Chemistry I or both. There are 40 sophomores taking French II but not Chemistry I, and 60 sophomores taking Chemistry I but not French II. How many sophomores are taking both French II and Chemistry I ? A.
There are 55 sophomores taking French II and Chemistry I.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
According to the given information, the required solution would be as:
First, we need to find the number of sophomores taking French II, Chemistry I, or both:
⇒ 1/3 × 465
Apply the multiplication operation, and we get
⇒ 155
Of the 155 sophomores, 40 are taking only French II and 60 are taking only Chemistry I:
⇒ 155 - 40 - 60
⇒ 155 - 100
Apply the subtraction operation, and we get
⇒ 55
Thus, there are 55 sophomores taking French II and Chemistry I.
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A triangle has one 42° angle and two 69° angles. Is this triangle scalene?
Step-by-step explanation:
It is not a scalene triangle
because the third angle is 69⁰
Explanation: 180-(69+42)
180-111
69
What is a formula for the nth term of the given sequence?
180, -240, 320...
im lost
the sales of a grocery store had an average of $8,000 per day. the store introduced several advertising campaigns in order to increase sales. to determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 75 days of sales was selected. it was found that the average was $8,250 per day. from past information, it is known that the standard deviation of the population is $1,200. what is the value of the test statistic? round your answer to three decimal places.
When the standard deviation is $1200 and the mean is $8000, the test statistic's result will be -1.804.
What is test statistic?A statistic employed in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single number that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed. A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.
Here,
The claimed mean=$8250
The actual mean=$8000
The sample size=75
The standard deviation=$1200
The test statistic,
=(Actual mean-claimed mean)/Standard deviation/√(sample size)
=(8000-8250)/1200/√75
=-250/1200*1/√75
=-1.804
The value of test statistic will be -1.804 when the mean is $8000 and standard deviation is $1200.
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For liner function f, f (2) = 0 and f (4) = -6.
Write function F in slope intercept form
How do you find the slope of the line when you have two points?
Answer:
Step-by-step explanation: y = -3x + 6
Nancy ran 8 miles. How many yards did she run?
Answer: Nancy ran, 14080 yards.
Step-by-step explanation:
need help on 10,12, and 13 please
Answer:
Step-by-step explanation:
Answer:
(10) x=1, y=-3
(12) x=3, y=22
(13) x= 6, y= 7
Step-by-step explanation:
[10] 6x -9 =-3x
6x+3x=9
9x=9
x=9,
Set 1 angles a and c are ? and are also ? Set 2 angles b and d are ? and are also?
2.
2.
1)
a = 62⁰
b
d
O
2)
b = 120°
a
d
question content area top part 1 one of the ancient stone pyramids in egypt has a square base that measures 148 m on each side. the height is 126 m. what is the volume of the pyramid?
The ancient stone pyramids in Egypt, which have a square base with a width of 148 meters and a height of 126 meters, have a volume of 9394 square metres.
What is volume?Mathematics uses cubic units to quantify volume, including cubic meters, cubic centimeters, cubic millimeters, etc. Typically, liters and gallons are used to calculate liquid volume. The loudness of a sound is measured by its volume. A container's capacity, or how much it can hold, would be determined by its volume. Cubic units established by the International System of Units are frequently used to express volume. Learn how to easily measure volume.
Here,
Side of the pyramid=148 m
Height of pyramid=126 m
Volume,
=1/2*b*h
=1/2*148*126
=9394 m²
The volume of the ancient stone pyramids in Egypt that has a square base of side 148 m and height 126m is 9394 m².
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I need help its hard pls
Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
Using the z-score a randomly selected Endure All battery has a 10.56% chance of lasting more than 550 hours.
What is the z-score?How closely a value relates to the mean of a set of values is measured using a Z-score.
Z-score is calculated using standard deviations from the mean.
When a data point's Z-score is 0, it indicates that its entire score is equal to the mean score.
So, how far the raw score deviates from the mean is determined using the Z score.
These steps are used to determine the Z score:
z = (x - μ)/σ
We know that: x > 550 and μ = 500, σ = 40
z = 550 - 500 / 40
z = 1.25
Using the normal distribution graph as a guide:
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Therefore, using the z-score a randomly selected Endure All battery has a 10.56% chance of lasting more than 550 hours.
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Which situation represents a proportional
relationship?
The cost of purchasing boxes of paper is
$25.39 per box plus a shipping fee of
$3.25.
The cost of repairing a copy machine is
is $35.75 per hour with a service charge
of $80.50
The only option that represents a proportional relationship is;
d) The cost of repairing a computer at $54.75 per hour
How to Interpret a Proportional Relationship?Proportional relationships are defined as relationships between two variables where their ratios are equivalent.
a) The cost of purchasing boxes of paper is $25.39 per box plus a shipping fee of $3.25. If the number of boxes are x, then;
y = 25.39x + 3.25
This does not represent a proportional relationship as their ratios are not equivalent.
b) The cost of repairing a copy machine is is $35.75 per hour with a service charge of $80.50. The equation is;
y = 35.75x + 80.50
This does not represent a proportional relationship as their ratios are not equivalent.
c) The cost of purchasing printer cartridges at $34.85 per cartridge including delivery. This is not a proportional relationship as the ratio is not a straightforward one based on the delivery.
d) This represents a proportional relationship because the equation is;
y = 54.75x
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The complete options are;
a) The cost of purchasing boxes of paper for $25.39 per box plus a shipping fee of $3.25 per box .
b) The cost of repairing a copy machine at $35.75 per hour with a service charge of $80.50
c) The cost of purchasing printer cartridges at $34.85 per cartridge including delivery
d) The cost of repairing a computer at $54.75 per hour
Ms.D bought 8 1/2 pounds of ham from Excellente Hambaked Shop. She gave 1 3/4 pounds of ham to Mr.Chavir. How many pounds of ham does she have left?
I have 13 nutcrackers and 14 snowmen on my tree. How many stars are there? Let s repentant the amount of stars.
Hint there is 29 in all.
Answer:
There are 2 stars
Step-by-step explanation:
There are 29 items in total.
As we are given the number of two of the items(nutcrackers and snowmen)we can easily find the number of the last item(stars) by subtracting the number of nutcrackers and snowman by the number of total items.(29)
So the solution would be :
29 - (13 + 14) = number of stars
==> add 13 and 14
29 - 27 = number of stars
==> simplify
2 = number of stars
this is due in 1 hour. please help!
an ice cream cone is filled with vanilla and chocolate ice cream at a ratio of 2:1. if the diameter of the cone is 2 inches and the height is 6 inches, approximately what is the volume of vanilla ice cream in the cone? (round to nearest tenth) responses a 6.3 in3in36.3 in 3 b 2.1 in3in32.1 in 3 c 1.0 in3in31.0 in 3 d 4.2 in3
The volume of the vanilla ice cream in the cone is 4.18 cubic inches
The diameter of the cone = 2 inches
The radius of the cone = 2/1
= 1 inches
The height of the cone = 6 inches
The volume of the cone = (1/3) × π × r^2 × h
Substitute the values in the equation
= (1/3)π × 1^2 × 6
= 6.28 cubic inches
The ratio of vanilla and chocolate ice cream = 2:1
2x + x = 6.28
3x = 6.28
x = 6.28 / 3
x = 2.09
The volume of vanilla ice cream = 2x
= 2×2.09
= 4.18 cubic inches
Therefore, the volume of vanilla ice cream is 4.18 cubic inches
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The graph shows the distance Caleb runs over time. Whats the slope of the line and the equation?
Answer:
slope = 1/8
equation: y = 1/8 x
Step-by-step explanation:
Let distance = y.
Let time = x.
y = mx + b
Look at point (1, 8).
Also, the line passes through (0, 0).
slope = m = 1/8
Since it is a direct proportion, b = 0.
Equation: y = 1/8 x
You have a bag with five different colored marbles in it; red, green, blue, orange, and purple. Each marble has an equal chance of
being drawn from the bag and a marble is replaced after each draw.
After four draws from the bag what is the probability that you have seen both the red and green marbles at least once?
The probability that you have seen both the red and green marbles at least once is 0.3104
Given,
1/5 chance of winning a marble of any color in a drawing.
Every draw is independent and has the same probability because the marbles are replaced.
Calculating = 1- the likelihood of not receiving both red and green marbles in any of the four draws yields the same result as P, the probability of receiving both red and green marbles at least once (Q).
The union of the following three examples represents ways to not receive both red and green in all four draws:
(1)
Probability of no red and no green in a draw = 3/5.
Probability of no red and no green in 4 draws,
Q1 = 3/5 * 3/5 * 3/5* 3/5 = 81/54
The probabilities are multiplied as each draw is independent and has the same probabilities.
(2)
The probability of no red and 1 green in 4 draws is given by binomial probability.
= (4 3) (1/5)(3/5)³ = (4 * 3³)/5¹ = 108/5⁴
The probability of no red and 2 green in 4 draws is given by binomial probability.
= (4 2) (1/5)²(3/5)² == (6 * 3²)/54 = 54/5⁴
The probability of no red and 3 green in 4 draws is given by binomial probability.
= (4 3) (1/5)³(3/5) == (4 * 3)/5¹ = 12/5⁴
The probability of no red and 4 green in 4 draws is given by binomial probability.
= (4 4) = 1 * 1/5¹ = 1/5⁴⁴
Q2= sum of all 4 above probabilities.
Q2 (108 +54 + 12+1)/5 = 175/5⁴
(3)
This probability is the same as in Q2. Q3 = 175/5⁴
Therefore the probability of not seeing both red and green at all,
Q = Q1 + Q2 + Q3.
= 81 +175 + 175/5⁴ = 413/5⁴
Finally, the probability of getting both red and green at least once,
P = 1 - Q
= 1-413/5⁴
= (625 431)/625
= 194/625
= 0.3104.
The answer is 0.3104.
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How do you say 7.793 in word
Answer:
seven and seven hundred nintey three thousandths
Step-by-step explanation:
What is the value of 4/15 divided by -3.4
Answer:
[tex]-\frac{4}{51}\approx-0.07843[/tex]
Explanation:
[tex]\frac{4}{15}(-\frac{1}{3.4})\\\frac{4}{15}(-\frac{5}{17})\\-\frac{20}{255}\\-\frac{4}{51}\approx-0.07843[/tex]
M is the midpoint of AC. A is (3, -9) and C is (-5, 16). Solve for the following
What is the midpoint M?
What is the length or distance of AC?
The coordinates of the midpoint are (-1, 3.5) and the distance of AC is 26.25 units.
How to find the coordinates of the midpoint?We know that for a segment whose endpoints are (x₁, y₁) and (x₂, y₂), the coordinates of the midpoint are:
( [x₁ + x₂]/2, [y₁ + y₂]/2)
In this case, the endpoints are: (3, -9) and (-5, 16), then the midpoint is:
M = ( [3 - 5]/2, [-9 + 16]/2)
M = (-1, 3.5)
The distance between two points (x₁, y₁) and (x₂, y₂) is:
d = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)
So here the distance is:
d = √( (3 + 5)^2 + (-9 - 16)^2) = 26.25 units.
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You are going to bake an oversized sheet cake. The recipe calls for 2 cups of sugar for every 3 cups of flour. How many cups of flour are needed if you use 18 cups of sugar? Which answer is correct?
(1): 27 cups
(2): 18 cups
(3): 9 cups
(4): 6 cups
Ari earned $356.74 the first week he
worked. The second week he earned
$427.19. To the nearest dollar ABOUT
how much less did he earn the first
week?
HELP ITS DUE TODAY!!!!!!
Answer: The second one (B)
Hope this helps! :)
Step-by-step explanation:
The times when Hayden made the bracelets in this situation don't matter. All that matters in this problem is how many he made. Since it tells you that he made them for 5 days, you would multiply the number of bracelets by the days, to get the total. (Or write the equation like so: 5*(2+4))
And of course, since they are divided into groups as the last step, we have division.
5*(2+4) /6
a family decides to have children until it has three chil-dren of the same gender. assuming p(b)5p(g)5.5, what is the pmf of x5the number of children in the family?
The pmf of X = the number of children in the family is
1/4 + 3/8 + 3/8 =1
It is given that,
a family decides to have children until it has three children of the same gender i.e. BBB or GGG.
X can take the values {3,4,5}
and we know that
P(X = 3) + P(X = 4) + P(X = 5) = 1
We will find each term one by one,
P(X = 3) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*2
= [tex]\frac{1}{8}[/tex] * 2
P(X = 3) = [tex]\frac{1}{4}[/tex]
P(X = 4) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*6
= ([tex]\frac{1}{16}[/tex]) * 6
P(X =4) = [tex]\frac{3}{8}[/tex]
P(X = 5) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*12
= ([tex]\frac{1}{32}[/tex])* 12
P(X = 5) = [tex]\frac{3}{8}[/tex]
Therefore the pmf equation implies,
[tex]\frac{1}{4} + \frac{3}{8} + \frac{3}{8}[/tex] = [tex]\frac{32}{32}[/tex] = 1.
The probability mass function (pmf) is also called a probbility function or frequency which characterizes the distribution of a discrete random variable. It is a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value.
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