The age of a father is 2 less than 7 times the age of his son. In 3 years, the sum of their ages will be 52. If the son’s present age is s years, which equation models this situation?
Answer:
Son’s present age, s = 6 years.
Step-by-step explanation:
Let the son’s present age is s years and father's be f.
We have age of a father is 2 less than 7 times the age of his son.
f = 7s -2
7s - f = 2 -------------------eqn 1
In 3 years, the sum of their ages will be 52.
s + 3 + f + 3 = 52
s + f = 46 -------------------eqn 2
eqn 1 + eqn 2
8s = 48
s = 6
Son’s present age, s = 6 years.
Anyone know this geometry question?
A manufacturer packages bolts in boxes containing 100 each. each box of 100 bolts contains on average four defective bolts. the quality control staff randomly selects a box at the end of the day from an entire production run. what is the probability that the box will contain less than three defective bolts? use the poisson distribution table.
Using Poisson Distribution, the probability that the box will contain less than three defective bolts is computed by adding up the probabilities of finding 0, 1, or 2 defective bolts in a box. The average occurrence rate is 4 defective bolts on average.
Explanation:Based on the provided details, we can conclude that this is a problem involving Poisson Distribution. The key parameters here are that the box contains 100 bolts and on average, 4 bolts are defective. The question asks for the probability that the box will contain less than three defective bolts, or in other words the probability that there are either 0, 1, or 2 defective bolts in a box. With a Poisson distribution, the formula to calculate the probability is P = lambda^k * exp(-lambda) / k! where lambda is the average occurrence rate, k is the number of occurrences of the event, and exp refers to the exponential function.
To calculate the probability of finding less than 3 defective bolts, we add together the probabilities of finding 0, 1, and 2 defective bolts using the above formula. In this example, lambda = 4 defective bolts on average, and we substitute k with 0, 1, and 2 respectively. Solve these cases separately and then add them up, that will give you the probability that a box will contain less than three defective bolts.
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Determine if the statement is always, sometimes, or never true: A scalene triangle is an acute triangle.
Answer:
it is true
Step-by-step explanation:
The scores of several classmates on a language arts test are shown below: 86 points 87 points 87 points 94 points 95 points 82 points 78 points 89 points 80 points 84 points What is the median score for these students? 87.5 points 87 points 86.5 points 86 points
Answer:
Your answer would be 87.5
Step-by-step explanation:
The reason that I know is because 87 is the most used number in this situation which it then makes it 87.5.
Answer:
87.5 would be the correct answer!
Step-by-step explanation:
if you follow every set of points then the median would be 87.5
Find all the solutions of the equation in the interval 0 2pi) 2sin2x=2+cosx
6. Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 147 of the first 156 customers have not received a star on their receipts. What is experimental probability of winning a free gallon of milk?
A. 11/156
B. 49/52
C. 2/39
D. 3/52*****?
[tex] |\Omega|=156\\
|A|=156-147=9\\\\
P(A)=\dfrac{9}{156}=\dfrac{3}{52}\implies \text{D} [/tex]
BRAINLIST ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. A wooden plank is leaning against an outside wall of a building. The bottom of the plank is 3 ft from the wall. Find each of the following values, and show all your work.
(a) Find the approximate length of the plank. Round to the nearest tenth of a foot.
(b) Find the height above the ground where the plank touches the wall. Round to the nearest tenth of a foot.
2. A support wire is strung from a tree. The bottom of the wire is 24 ft from the tree. The length of the wire is 30 ft. Find each of the following values, and show all your work.
(a) Find the value of x. Round to the nearest tenth of a degree.
(b) Find the approximate height where the wire touches the tree. Round to the nearest foot.
you buy a circular rug with a diameter of 8 feet how much floor space for the rug cover
The circular rug with a diameter of 8 feet covers approximately 50.27 square feet of floor space. This was calculated by finding the area of the circle using the formula πr².
Explanation:The question refers to how much floor space a circular rug with a diameter of 8 feet will cover. To solve this, you need to calculate the area of the circle. The formula for the area of a circle is πr², where r is the radius of the circle. But we were given the diameter, which is twice the radius. So the radius of the rug is 8/2 = 4 feet.
Substitute r=4 into the formula: Area = π(4²) = 16π square feet. Therefore, the circular rug covers 16π, or approximately 50.27 square feet of floor space.
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In the diagram below what is the approximate length of the minor arc XY
Answer:
B. 6.3 cm
Step by step explanation:
We have been given measure of central angle which intercepts to our minor arc XY.
Since we know that the formula to find measure of arc length is:
[tex]\text{Arc length}=\frac{\theta}{360}\times \text{circumference of circle}[/tex]
[tex]\text{Arc length}=\frac{\theta}{360}\times {2\pi r}[/tex]
Now let us substitute our given values in above formula.
[tex]\theta=40^{o}[/tex] and [tex]radius=9 cm[/tex]
[tex]\text{Arc length}=\frac{40}{360}\times {2\pi \cdot 9}[/tex]
[tex]\text{Arc length}=\frac{1}{9}\times {2\pi \cdot 9}[/tex]
[tex]\text{Arc length}=2 \pi [/tex]
[tex]\text{Arc length}=6.2831853071795865\approx 6.3[/tex]
Therefore, length of minor arc XY is 6.3 cm and option B is the correct choice.
If f(x)=2x and g(x)=x^{2}-1, which statement is true?
a) 2x^{2}-1
b) 2x(x^{2}-1)
c) 4x-1
d) 4x^{2}-1
Determine whether the polynomial is a difference of squares and if it is, factor it. y2 – 16
(y – 4)(y + 4) it is a difference this is it. I did the test just a second ago.
Which of the following sequences of numbers are arithmetic sequences?
Check all that apply.
A.2, 4, 6, 8, 10, ...
B.1, 1, 1, 1, 1, ...
C.1, 2, 3, 5, 6, 7, ....
D.3.0, 3.1, 3.2, 3.3, 3.4, ...
E.2, -4, 6, -8, 10, ...
Solve for x: x^2-36=0
Answer:
-6, 6
Step-by-step explanation:
BRAINLIEST IF RIGHT
The image represents what geometric construction?
A) Copy an angle construction
B) Parallel lines construction
C) Copy a segment construction
D) Perpendicular from a point not on the line
Without the visual reference of an image, the specific geometric construction represented can not be accurately determined. The provided options relate to different types of geometric constructions. These include copying angles, constructing parallel lines, copying segments, and creating perpendiculars from a point not located on a line.
Explanation:The geometric construction represented by the image is not entirely clear without an image. However, if we are to interpret the options, we can make some educated assumptions. Copy an angle construction involves replicating an existing angle in a new location. A parallel lines construction typically involves creating a line parallel to an existing one. To copy a segment construction, you would reproduce a particular line segment. The option of creating a perpendicular from a point not on the line would typically involve making a line perpendicular to an existing line from a specific point not originally on that line. Without the image, we can't definitively answer the question.
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Use a scientific calculator to find the logarithm for each number rounded ro four decimal places. Then state characteristic and the mantis.
12
A. 2.3855; -2 0.9564
B. 1.0793; 1; 0.0792
C. 0.5648; 0; 0.5648
D. -1.0458 -2; 0.0542
In 2011, the U.S. Centers for Control and Prevention (CDC) conducted a survey to track a wide variety of risky behavior by American youth. The following table summarizes the responses of 12^th grade males and females and their helmet wearing habits
according to the model which of the following temperatures to the nearest tenth of a degree would make the ice cream shop have a positive profit?
what expression is equivalent to 20+8y-9y-21
Final answer:
The expression equivalent to 20+8y-9y-21 is simplified by combining like terms, resulting in -1y - 1 or simply -y - 1.
Explanation:
To find an expression that is equivalent to 20+8y-9y-21, we need to combine like terms. The terms 8y and -9y are like terms because they have the same variable raised to the same power. The terms 20 and -21 are also like terms because they are both constants.
Combine the like terms:
8y - 9y = -1y
20 - 21 = -1
Now, put the simplified terms together:
-1y - 1
Therefore, the expression that is equivalent to 20+8y-9y-21 is -1y - 1, which can also be written as -y - 1.
Dylan wants to construct the midpoint M of RS which diagram shows a way Dylan can accurately construct M using only a compass and a straight edge
Given a point and a plane, how do you find a line that is parallel to the plane that passes through the point?
Area is the distance around a shape while perimeter is the space within a shape.
a) true
b) false
The scatter plot shows the relationship between the number of hours spent jogging and the number of minutes spent stretching, by the students on a track team:
A scatter plot is shown titled fitness routine. The x-axis is labeled hours jogging and the y-axis is labeled minutes stretching. Data points are located at 0 and 1, 2 and 1, 2 and 2, 4 and 3, 4 and 5, 6 and 3, 7 and 5, 9 and 4. A line connects the points 0 comma 1 and 10 comma 6.
What is the y-intercept of the line of best fit and what does it represent? (4 points)
1 minute; the number of minutes students stretch when they do not jog
1 hour; the number of hours students jog when they do not stretch
4 hours; the number of hours students jog when they do not stretch
4 minutes; the number of minutes students stretch when they do not jog
4.
(06.04)
The line of best fit for a scatter plot is shown:
A scatter plot and line of best fit are shown. Data points are located at 0 and 1, 2 and 1, 2 and 3, 4 and 3, 4 and 5, 6 and 3, 7 and 5, 9 and 4. A line of best fit passes through the y-axis at 1 and through the point 4 and 3.
What is the equation of this line of best fit in slope-intercept form? (4 points)
y = 1x + one half
y = one halfx + 1
y = 1x − one half
y = negative one halfx + 1
5.
(06.04)
The graph shows the number of cakes sold at Karen's Cake Shoppe for each of their 7 weeks in business:
A scatter plot is shown with the title Karens Cake Shoppe. The x axis is labeled Weeks in Business, and the y axis is labeled cakes sold. The data points are located at 1 and 2, 2 and 4, 3 and 5, 4 and 4, 5 and 6, 6 and 5, and 7 and 8. A line of best fit passes through the y axis at 1 and through the point 10 and 10.
If her current pattern continues, how many cakes will Karen most likely sell in her 10th week of business? (4 points)
10, because approximately y = 9 over 10.x + 1
11, because approximately y = 9 over 10.x + 1
8, because approximately y = 1x − 1
12, because approximately y = 1x + 2
The y-intercept in the first scenario represents the estimated stretching time if no jogging is done. In the second situation, the line of best fit equation shows that for each additional hour of jogging, an extra half minute of stretching is estimated. In the third scenario, Karen is predicted to sell about 12 cakes on her tenth week of operation.
The subject of this question is mathematics, specifically the concept of scatter plots and the line of best fit in linear regression. In the first scenario, the y-intercept of the line of best fit is 1 minute, which represents the estimated amount of time a student would spend stretching if they did not jog at all.
In the second scenario, the equation of the line of best fit is y = 0.5x + 1. This equation represents a relationship between the number of hours spent jogging (x) and the estimated minutes of stretching (y), where for every one extra hour of jogging, it is estimated that an additional half a minute is spent stretching.
Lastly, in the third scenario, using the line of best fit, Karen will likely sell approximately 12 cakes because the line of best fit is approximately y = 1x + 2, and substituting 10 for x (10th week), we get 12 (cakes).
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For the standard normal curve, find the z-score that corresponds to the 90th percentile.
which of the following expressions is the inverse of the function
[tex]y = \frac{x - 2}{3} [/tex]
Given: Circle M with inscribed and congruent radii JM and ML Prove: m = What is the missing reason in step 8? Statements Reasons 1. circle M with inscribed ∠KJL and congruent radii JM and ML 1. given 2. △JML is isosceles 2. isos. △s have two congruent sides 3. m∠MJL = m∠MLJ 3. base ∠s of isos. △are ≅ and have = measures 4. m∠MJL + m∠MLJ = 2(m∠MJL) 4. substitution property 5. m∠KML = m∠MJL + m∠MLJ 5. measure of ext. ∠ equals sum of measures of remote int. ∠s of a △ 6. m∠KML =2(m∠MJL) 6. substitution property 7. 7. central ∠ of △ and intercepted arc have same measure 8. 8. ? 9. 9. multiplication property of equality reflexive property substitution property base angles theorem second corollary to the inscribed angles theorem Mark this and return
Answer:
substituition property
Step-by-step explanation:
What is the measure of ∠P ? Round your answer to the nearest degree.
A.) 29°
B.) 42°
C.) 65°
D.) 78°
Answer:
B. [tex]42^{\circ}[/tex]
Step-by-step explanation:
We have been given an image of a triangle. We are asked to find the measure of angle P.
We will use law of sines to solve for angle P.
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex], where a, b and c are the sides corresponding to the angles A, B and C.
Upon substituting our given values we will get,
[tex]\frac{sin(P)}{QR}=\frac{sin(Q)}{PR}[/tex]
[tex]\frac{sin(P)}{47.6}=\frac{sin(73^{\circ})}{68}[/tex]
[tex]\frac{sin(P)}{47.6}=\frac{0.956304755963}{68}[/tex]
[tex]\frac{sin(P)}{47.6}=0.01406330523475[/tex]
[tex]\frac{sin(P)}{47.6}\times 47.6=0.01406330523475\times 47.6[/tex]
[tex]sin(P)=0.6694133291741[/tex]
Now we will use arcsin to find the measure of angle P.
[tex]P=sin^{-1}(0.6694133291741)[/tex]
[tex]P=42.021801403079^{\circ}\approx 42^{\circ}[/tex]
Therefore, the measure of angle P is 42 degrees and option B is the correct choice.
Help Please thank you!
PLS HELP! THIS IS FOR STATE TESTS TOMORROW!! Shannon has a garden that is 18 by 27 feet. Find the perimeter of the garden. Please submit your answer and explain how to find the perimeter.
PLEASE HELP ME FAST I WILL GIVE BRAINLIEST TO BEST AND FASTEST ANSWER
Perform the indicated operation.
(6f 2 - 13 - 11f) ÷ (3f - 4)
2f + 1 R 17
2f - 1 R -17
2f - 1
If you would like please tell me what the R means
Answer: 2f - 1, remainder -17
Step-by-step explanation:
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