Answer:
[tex]\frac{24}{65}[/tex]
Step-by-step explanation:
Total number of students in the class = 26
Number of boys in the class = 10
Number of girls in the class = 26 - 10 = 16
The formula for probability is :
[tex]\text{Probability}=\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}[/tex]
In this case the favorable outcomes would be the number of girls in the class and total outcomes would be the total number of students in the class.
Eduardo has to pull out two names from the hat. Since there are 16 girls in the class of 26, the probability that the first name will be of the girl will be = [tex]\frac{16}{26}[/tex]
After picking up the 1st name, there would be 25 names in the hat with 15 names of girls as one of the girl is already been chosen. So,
The probability that the second name would belong to a girl = [tex]\frac{15}{25}[/tex]
The probability that both the partners will be girls will be equal to the product of two individual probabilities as both the events are independent.
Therefore,
The probability that both of Eduardo's partners for the group project will be girls = [tex]\frac{16}{26} \times \frac{15}{25} = \frac{24}{65}[/tex]
Jimmy's sister is twice as old as he is. His big brother is 5 years older than he is. The sum of their three ages is 29 . How old is Jimmy's brother?
Answer:
11 years old
Step-by-step explanation:
Let Jimmy's age be represented as x. His big brother's age is x+5 and his sister's age is 2x. Adding these gives us 4x+5=29. Solving for x gives us 6. His brother's age is 6+5=11.
11 years old is Jimmy's brother.
Let Jimmy's age be represented as x. His big brother's age is x+5 and his sister's age is 2x. Adding these gives us 4x+5=29. Solving for x gives us 6. His brother's age is 6+5=11.
J=Jimmy's age; S=sister's age=2J; B=brother's age=J+5
.
J+S+B=29
J+(2J)+(J+5)=29
4J+5=20
4J=24
J=6
Jimmy is 6 years old.
B=J+5=6+5=11
ANSWER: Jimmy's brother is 11 years old.
.
CHECK:
S=2J=2(6)=12
Jimmy's sister is 12 years old.
.
J+S+B=29
6+12+11=29
29=29.
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Solve for x in the equation x^2+20x+100=36
a).x = –16 or x = –4
b).x = –10
c).x = –8
d).x = 4 or x = 16
Answer:
a
Step-by-step explanation:
Given
x² + 20x + 100 = 36 ( subtract 36 from both sides )
x² + 20x + 64 = 0 ← in standard form
Consider the factors of the constant term ( + 64) which sum to give the coefficient of the x- term ( + 20)
The factors are + 16 and + 4, since
16 × 4 = + 64 and 16 + 4 = + 20, hence
(x + 16)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 16 = 0 ⇒ x = - 16
x + 4 = 0 ⇒ x = - 4
A compact minivan costs $16,000 with a residual value of $1,000. It has an estimated useful life of five years. If the minivan was bought on July 3, what would be the book value at the end of Year 1 using straight-line rate? A. $14,500 B. $16,000 C. $1,500 D. $12,500
Answer:
A. $14,500
Step-by-step explanation:
The van depreciates ($16000 -1000 = $15000 in 5 years, so $3000 per year. It will be assumed to depreciate half that amount in half a year, so will be worth $1500 less than $16000 at the end of the first calendar year. The book value will be $14,500.
Final answer:
The book value of the minivan at the end of Year 1 is $14,500 after accounting for 6 months of straight-line depreciation of $1,500 from the original cost of $16,000.
Therefore, the correct answer is A. $14,500.
Explanation:
The student's question is related to calculating the book value of a minivan at the end of year 1 using the straight-line depreciation method. To find the book value, we need to first calculate the annual depreciation expense and then subtract it from the original cost of the minivan.
First, we calculate the annual depreciation expense:
Purchase price of minivan: $16,000
Residual value: $1,000
Useful life: 5 years
So, the annual depreciation expense is
(
$16,000
-
$1,000
) /
5 years
= $3,000 per year.
Since the minivan was bought on July 3, we need to account for a partial year of depreciation for year 1. Assuming the end of the year is December 31, that's 6 months (July through December) of depreciation in the first year. Therefore, it would be
$3,000 / 2 = $1,500 for 6 months.
To find the book value at the end of Year 1, we subtract the depreciation for the first 6 months from the purchase price:
$16,000 - $1,500 = $14,500.
A restaurant offers a $12 dinner special that has 6 choices for an appetizer, 12 choices for an entrée, and 3 choices for a dessert. How many different meals are available when you select an appetizer, an entrée, and a dessert?
There are 216 different meals available when you select an appetizer, an entrée, and a dessert from the restaurant's menu.
Given that there are 6 choices for the appetizer, 12 choices for the entrée, and 3 choices for the dessert.
Total number of choices:
6 (choices for appetizer) × 12 (choices for entrée) × 3 (choices for dessert) = 216 different meals
Therefore, there are 216 different meals available when you select an appetizer, an entrée, and a dessert from the restaurant's menu.
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There are 216 possible meals. This answer is obtained by applying the counting principle in mathematics, which multiplies together the choices for each part of the meal (appetizer, entrée, dessert).
Explanation:This problem regards the counting principle in mathematics, which is a way of finding the total number of possible outcomes for a series of events. In this case, the events are choosing an appetizer, entrée, and dessert. The counting principle tells us that we can find the total number of possible meals by multiplying together the number of choices for each part of the meal.
Thus, we can solve this problem as follows:
Select an appetizer: 6 choices.Select an entrée: 12 choices.Select a dessert: 3 choices.By the counting principle, we multiply these together to get the total number of possible meals: 6 * 12 * 3 = 216 meals.
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Use the figure to find the trigonometric ratio below. Express the answer as a decimal rounded to the nearest ten-thousandth.
sin B
CB = , AD = 25, CD = 5, DB = 1
Question 2 options
0.9806
5
1.0198
0.1961
Answer:
The correct option is 1.
Step-by-step explanation:
Given information: AD = 25, CD = 5, DB = 1 and CD⊥AB.
According to the Pythagoras theorem,
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
In triangle BCD,
[tex]CB^2=DB^2+CD^2[/tex]
[tex]CB^2=1^2+5^2[/tex]
[tex]CB^2=26[/tex]
Taking square root both sides.
[tex]CB=\sqrt{26}[/tex]
In a right angled triangle,
[tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]
[tex]\sin B=\frac{CD}{CB}[/tex]
[tex]\sin B=\frac{5}{\sqrt{26}}[/tex]
[tex]\sin B=0.980580675691[/tex]
[tex]\sin B\approx 0.9806[/tex]
Therefore the correct option is 1.
Answer:
0.9806 is the correct answer.
Step-by-step explanation:
You want to put a 5 inch thick layer of topsoil for a new 16 ft by 34 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answer: About 8.5 cubic yards
Step-by-step explanation:
Given : The length of the garden = 16 ft.
The width of the garden = 34 ft.
The depth of the thick layer of topsoil on the garden = 5 inch
=[tex]\dfrac{5}{12}\text{ ft.}[/tex] [Since 1 foot = 12 inches]
The volume of a rectangular prism :-
[tex]V=l*w*h[/tex], where l is length , w is width and h is height.
The number of cubic feet of topsoil required will be
[tex]V=16\times34\times\dfrac{5}{12}=\dfrac{680}{3}\text{cubic feet}[/tex]
Since 1 yard = 3 feet
[tex]1\text{ foot}=\dfrac{1}{3}\text{ yard}[/tex]
[tex]V=\dfrac{680}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}=8.3950617284\approx8.50\text{cubic yards}[/tex]
A level of measurement describing a variable whose attributes are rank-ordered and have equal distancesbetween adjacent attributes are _____ measures. interval ratio nominal theoretical ordinal
Answer: ordinal
Step-by-step explanation:
There are 4 levels of measurements scales :-
1. Nominal scale : It is used when we categorize the data on the basis of the characteristic such as Religion, Gender , etc.
2. Ordinal scale : It is used when we can order attributes according to their ranks. For example : First > Second > Third and so on.
3. Interval scale : It provides the characteristic of the difference between any two categories. For example : Fahrenheit scale to measure temperature.
4. Ratio scale : It has all the qualities of nominal, ordinal, and interval measures and in addition a "true zero" point. For example : Age.
From the above definitions , A level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes are ordinal measures.
A rectangle is 5 times as long as it is wide. The perimeter is 70 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary. a. 14 cm by 70 cm c. 11.7 cm by 29.2 cm b. 5.8 cm by 64.2 cm d. 5.8 cm by 29.2 cm
Let the width = X, then the length would be 5x ( 5 times as long as the width).
The perimeter is adding the 4 sides.
x + x + 5x + 5x = 70
Combine the like terms:
12x = 70
Divide both sides by 12:
x = 70/12
x = 5.83
The width = 5.83 cm.
The length = 5 x 5.83 = 29.15
Now round each length to the nearest tenth:
5.8 and 29.2 cm.
The answer is d.
In a right triangle the lengths of the legs are a and b. Find the length of the hypotenuse, if: a=3/7, b=4/7
Answer:
5/7
Step-by-step explanation:
We need the Pythagorean Theorem here.
If you have a right triangle, you can use the equation a^2+b^2=c^2 where a and b are legs and c is the hypotenuse.
Plug in your information.
(3/7)^2+(4/7)^2=c^2
Simplify what you can.
9/49+16/49=c^2
25/49=c^2
Square root both sides.
5/7=c
Answer:
5/7.
Step-by-step explanation:
Let the hypotenuse = h , then:
h^2 = (3/7)^2 +(4/7)^2 ( By the Pythagoras Theorem).
h^2 = 9/49 + 16/49
h^2 = 25/49
h = 5/7.
Can someone also help me on this one!!
The change in the X values is in multiples of 2.
The change in the h(x) values need to be: -0.3 x 2 = -0.6
Now find the h(x) values that have a difference of -0.6
A negative value is a decrease.
2 to 4 is an increase.
4 to 6 is an increase.
6 to 8 is an increase.
8 to 10 is an increase.
10 to 12 = 20-19.8 = 0.2
12 to 14 = 19.8 - 19.2 = 0.6
The two columns are 12 and 14
URGENT!! Offering 39 Points
The solution to this system of equations lies between the x-values -2 and -1.5. At which x-value are the two equations approximately equal?
Answer:
D. -1.8
Step-by-step explanation:
A graphing calculator can show you this easily, as can any calculator or spreadsheet that helps you evaluate the functions at different values of x.
The graphs cross at approximately x = -1.8.
Answer:
Step-by-step explanation:
d
Analyze the diagram below and complete the instructions that follow.
If mZK = 82°, find mZL, M2M, and mZN.
A. m L = 82°, m_M= 82°, m N=98°
B. MZL = 82°, mZM = 989, m N= 98°
C. mL = 98°, mM= 82°, m N= 98°
D. MZL = 98°, mZM = 98°, mZN= 82°
Answer:
c
Step-by-step explanation:
C is your answer. Since this is a parallelogram, is means that there are two sets of sides with the same length. Because the measurement of angle K is 82 the angle directly opposite would have the same measurement. That's why angle M is also 82. When you add all the angles of a quadrilateral it adds up to 360 degrees. multiply 82 by 2 to get 164 and subtract that from 360 to get 196. you then have to divide that by 2 and you will get 98 which is the measurement for both angles L and N
Answer:
The correct answer is option C.
m<L = 98°, m<M = 82° and m<N = 98°
Step-by-step explanation:
From the figure we can see a parallelogram KLMN
Properties of parallelogram
1)Opposite sides are equal and parallel.
2) Opposite angles are equal.
3) Adjacent angles are supplementary.
To find the correct option
It is given that, m<K = 82°
By using properties of parallelogram we get
m<L = 98°, m<M = 82° and m<N = 98°
Therefore the correct answer is option C
Describe the composite transformation that has occurred.
Answer:
rotate CCW 90°, reflect across the x-axis(x, y) ⇒ (-y, -x) . . . . . both transformations togetherStep-by-step explanation:
The vertex order ABC is clockwise in the original figure and also in the first image: A'B'C'. The altitude from AC to B is up in the original and left in the first image, indicating a rotation 90° CCW.
The first transformation is a rotation 90° CCW.
The vertex order of A''B''C'' is CCW, indicating a reflection. The direction of the altitude from A''C'' to B'' is still to the left, so the reflection must be over a horizontal line. We find the x-axis bisects the segments A'A'', B'B'', and C'C'', confirming that it is the line of reflection.
The second transformation is reflection across the x-axis.
_____
Algebraically, the transformations are ...
1st: (x, y) ⇒ (-y, x)
2nd: (x, y) ⇒ (x, -y)
Both together: (x, y) ⇒ (-y, -x).
Carol uses this graduated tax schedule to determine how much income tax she owes.If Carol’s taxable income is $89,786, how much income tax does she owe, to the nearest dollar?
If Carol’s taxable income is $89,786, how much income tax does she owe, to the nearest dollar?
a.
$25,140
b.
$12,654
c.
$19,636
d.
$37,626
Answer:
C
Step-by-step explanation:
The answer is C
Answer:
Your answer would be C
Step-by-step explanation:
I got it right on edge <3
Please help question attached
Answer:
a = sqrt( 3x+1)
Step-by-step explanation:
f(x) = sqrt(x-1)
g(x) = 3x+2
(f°g)(x) means replace g(x) in f(x) every place you see an x
(f°g)(x) = sqrt( g(x) -1)
= sqrt( 3x+2 -1)
Simplifying
=sqrt( 3x+1)
8. A tourist boat is used for sightseeing in a nearby river. The boat travels 2.4 miles downstream and in the same amount of time, it travels 1.8 miles upstream. If the boat travels at an average speed of 21 miles per hour in the still water, find the current of the river.
Answer:
3 mph
Step-by-step explanation:
Let c represent the current of the river in miles per hour. Then the ratio of speed downstream to speed upstream is ...
(21 +c)/(21 -c) = 2.4/1.8
1.8(21 +c) = 2.4(21 -c) . . . . . . multiply by 1.8(21-c)
37.8 + 1.8c = 50.4 -2.4c . . . . eliminate parentheses
4.2c = 12.6 . . . . . . . . . . . . . . . add 2.4c-37.8
c = 3 . . . . . . . . . . . . . . . . . . . .divide by 4.2
The current of the river is 3 miles per hour.
Identify the number as real, complex, pure imaginary, or nonreal complex. (more than one of these descriptions may apply.)−7
Answer:
-7 is real and complex
Step-by-step explanation:
Every number is complex.
Complex numbers are in the form of a+bi where a and b are real numbers.
Pure imaginary are complex numbers with a being 0.
Real numbers are complex number with b being 0.
-7 is a real number and a complex number.
(It doesn't have an imaginary part)
-7 is a real and complex number.
What are the different types of numbers?A real number is a value of a continuous quantity that can represent a distance along a line.The real numbers include all the rational numbers (positive, negative, fraction -4,-3,2,3,4/3,-6/7, etc)The real numbers are all irrational numbers, such as square root, cube root, etc.Real numbers are complex numbers with 0.Pure imaginary numbers are complex numbers with a being 0.Complex numbers are in the form of (x+yi) where a and b are real numbers.Every number is a complex number.Learn more about numbers here:-https://brainly.com/question/148825
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Please help math!!! pic below
Answer:
a) 47.5 millionb) 65.2 millionc) 72 millionStep-by-step explanation:
It is convenient to let a spreadsheet or graphing calculator do the repetitive evaluation of a function like this. That simplifies the work and reduces errors.
The function is shown in the attachment written in Horner form, which is convenient for evaluation by hand or using a calculator.
A bag Contains rubber bands with lengths that are normally distributed with a mean of 6 cm of length, and a standard deviation of 1.5 cm. What is the probability that a randomly selected nail is between 4.5 and 7.5 cm long?
Answer:
0.68
Step-by-step explanation:
Given
Mean = μ = 6 cm
SD = σ = 1.5 cm
We have to find the z-scores for 4.5 and 7.5
z-score for 4.5 = z_1 = (x-μ)/σ = (4.5-6)/1.5 = -1.5/1.5 = -1
z-score for 4.5 = z_2 = (x-μ)/σ = (7.5-6)/1.5 = 1.5/1.5 = 1
We have to find area to the left of z-scores
Using the rule of thumb for SD from mean, 68% of data lies between one standard deviation from mean. So the probability of choosing a band with length between 4.5 and 7.5 cm is 0.68 ..
A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 13% chose chocolate pie, and the margin of error was given as + or -4 percentage points. Given specific sample data, which confidence interval is wider: the 95% confidence interval or the 80% confidence interval? Why is it wider?
Answer:
95%
Step-by-step explanation:
For a given sample data, the width of the confidence interval would vary directly with the confidence level i.e. more the confidence level, wider will be the confidence interval.
This is because the critical value associated with the confidence level(e.g z value) becomes larger as the confidence level is increased which results in an increased interval.
The confidence interval for a population proportion is given by the formula:
[tex]p \pm z\sqrt{\frac{pq}{n} }[/tex]
So, for a fixed value of p,q and n, the larger the value of z the wider will be the confidence interval.
Hence 95% confidence interval will be wider than 80% confidence interval.
The 95% confidence interval is wider than the 80% confidence interval because it includes a larger area under the curve of a normal distribution, offering a higher level of confidence the true population parameter falls within this range.
Explanation:In statistical analysis, especially for polls like the one mentioned about favorite pies, the confidence interval plays a significant role in interpreting the reliability of the results. The 95% confidence interval is wider than the 80% confidence interval. This is because a higher confidence level, in this case 95%, means we are more sure that the actual population parameter lies within the interval, but in order to gain this certainty, the interval necessarily needs to be wider.
This can also be understood in the context of a normal distribution. For a 95% confidence interval, we are including a larger area under the curve of the distribution, thus the interval has to be wider than the one for the 80% confidence interval, which covers a smaller area.
It's important to note, however, that a wider confidence interval doesn't necessarily imply better predictability. It simply means there's a higher level of confidence that the true population parameter falls within the specified range.
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given the expression (7-4i)-(2+6i), perform the indicated operation and write the answer in the form a+bi
Answer:
[tex]5-10i[/tex]
Step-by-step explanation:
we know that
To subtract two complex number, subtract the real parts and subtract the imaginary parts
so
[tex](a+bi)-(c+di)=(a-c)+(b-d)i[/tex]
we have
[tex](7-4i)-(2+6i)[/tex]
so
[tex](7-4i)-(2+6i)=(7-2)+(-4-6)i=5-10i[/tex]
Solve for the volume using the equation: v = c[tex]x^{3}[/tex] divided by 6[tex]\pi[/tex][tex]^{2}[/tex]
(v = volume, c = circumference)
1. Circumference: 65.4 cm
2. Circumference 65.3 cm
3. Circumference 65.5 cm
Answer:
4723.6994 cm³4702.0641 cm³4745.4009 cm³Step-by-step explanation:
Put the numbers in the formula and do the arithmetic. For repetitive calculations, it is convenient to define a function in a graphing calculator or spreadsheet.
Identify the area of ⊙M in terms of π. HELP ASAP!!
Answer:
A = 196 pi m^2
Step-by-step explanation:
The area of a circle is given by
A = pi * r^2
The radius is 14
A = pi *14^2
A = 196 pi m^2
Answer:
196π m2
Step-by-step explanation:
A(n) _______ angle of a triangle is equal to the sum of the two remote interior angles.
-Exterior
-Interior
-Complementary
-Vertical
Answer:
Exterior
Step-by-step explanation:
In any triangle an exterior angle is equal to the sum of the two opposite interior angles.
Sabra went for a long hike and burned 845 calories in 3 1/4 hours.Nelson decided to go for a bike ride. He burned 1,435 calories in 4 7/8 hours.Who burned the most calories per hour?
Answer:
Nelson burned the most calories per hour
Explanation:
To solve this question, we will get the amount calories burned by each in one hour and then compare the two values
To do this, we will divide the total amount of calories burned by the total time
1- For Sabra:
We are given that she burnt 845 calories in [tex]3\frac{1}{25}[/tex] (which is equivalent to 3.25) hours
Therefore:
Calories burnt in an hour = [tex]\frac{845}{3.25}=260[/tex] calories/hour
2- For Nelson:
We are given that he burnt 1435 calories in [tex]4\frac{7}{8}[/tex] (which is equivalent to 4.875) hours
Therefore:
Calories burnt in an hour = [tex]\frac{1435}{4.875}=294.36[/tex] calories/hour
3- Comparing the two values:
From the above calculations, we can deduce that Nelson burned the most calories per hour
Hope this helps :)
Answer:
Nelson burned more cal/hr than Sabra at a rate of 294.36 cal/hr.
Step-by-step explanation:
To find out how many calories per hour each person burned, divide the amount of calories they burned by the amount of hours they spent exercising.
Sabra: 845 cal / 3.25 hr = 260 cal/hr
Nelson: 1435 cal / 4.875 hr = 294.36 cal/hr
260 < 294.36, so Nelson burned more calories/hour than Sabra.
URGENT!! Offering 50 Points
Approximate the solution to the equation using three iterations of successive approximation. Use the graph below as a starting point.
Answer:
B. x ≈ 13/8
Step-by-step explanation:
We assume that one iteration consists of determining the midpoint of the interval known to contain the root.
The graph shows the functions intersect between x=1 and x=2, hence our first guess is x = 3/2.
Evaluation of the difference between the left side expression and the right side expression for x = 3/2 shows that difference to be negative, so we can narrow the interval to (3/2, 2). Our 2nd guess is the midpoint of this interval, so is x = 7/4.
Evaluation of the difference between the left side expression and the right side expression for x = 3/4 shows that difference to be positive, so we can narrow the interval to (3/2, 7/4). Our 3rd guess is the midpoint of this interval, so is x = 13/8.
_____
The sign of the difference at this value of x is still negative, so the next guess would be 27/16. It is a little hard to tell what the question means by "3 iterations." Evaluating the function for x=13/8 will be the third evaluation, so the determination that x=27/16 will be the next guess might be considered to be the result of the 3rd iteration.
Answer:
B. x=13/8
Step-by-step explanation:
#platofam
Kendra is putting up a new fence around a rectangle or playground that measure 25 feet by 37 feet. If fencing costs 75.00 per foot how much will she have left over if she begins with 10,000?
Answer: She will have $700 left over.
Step-by-step explanation: Since we know that a rectangle has two sides with the measurement, we can add the sides. 37+37+25+25=124. The fencing in 124 feet in total. Multiply the 124 feet by the price per foot. 124 x 75 =9,300. Subtract the price from your total amount of money. 10,000 - 9,300 = $700. She will have $700 left over.
Answer:
there would be $700 left over
Step-by-step explanation:
1/2[sin(2θ + 7θ) + sin(2θ - 7θ)] = _____
cos2θcos7θ
cos2θsin7θ
sin2θcos7θ
sin2θsin7θ
Answer:
= 1/2[sin2Acos7A + cos2Asin7A + sin2Acos7A - cos2Asin7A]
we cut out
cos2Asin7A - cos2Asin7A
then we have
=1/2[sin2Acos7A + sin2Acos7A ]
= 1/2*2[ sin2Acos7A ]
cut out 2 we get
#sin2Acos7A
Geometry question, (photo inside)
Simplify the polynomial expression given below.
(2x − 1)(2x2 + 5x + 3) + (3x + 6)
Answer:
[tex]4x^{3}+8x^{2} +4x+3[/tex]
Step-by-step explanation:
Hello
To simplify the polynomial we must eliminate the parentheses
by definition
[tex]ax^{n}*bx^{m} =abx^{n+m}[/tex]
[tex](2x-1)(2x^{2} +5x+3)+(3x+6)\\(4x^{3} +10x^{2} +6x-2x^{2} -5x-3)+(3x+6)\\\\We\ add\ the\ similar\ terms\\\\(4x^{3}+8x^{2} +x-3)+(3x+6)\\\\4x^{3}+8x^{2} +4x+3[/tex]
I hope it helps
Have a great day
Answer:
Its A
Step-by-step explanation:
Just took it.