The speed at which the bottom of the ladder is being pulled away from the wall is equal to the rate at which the top is sliding down, which is 1 ft/second.
The bottom of the ladder is being pulled away from the wall at the same rate at which the top of the ladder is sliding down the wall. As the top of the ladder slides down at a rate of 1 ft/second, the bottom of the ladder is also being pulled away at a rate of 1 ft/second.
The bottom of the ladder is being pulled away from the wall at a rate of 100 ft/second if the top of the ladder is sliding down at a rate of 100 ft/second.
The speed at which the bottom of the ladder is being pulled away from the wall is equal to the rate at which the top is sliding down, which is 1 ft/second.
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Simplify.
hele mode
pharmill Bel
adicale
aps
x ².x1.x6 = x²
The expression x⁻². x⁻¹.x⁶ can be simplified as x³.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
x⁻². x⁻¹.x⁶
Simplify the expression,
By using multiplying property,
x⁻²⁺⁽⁻¹⁾⁺⁶
x ⁻²⁻¹⁺⁶
x⁻³ ⁺ ⁶
x³
The simplified form of the expression x⁻². x⁻¹.x⁶ is x³.
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How do u do this????
Let's consider what the question asks for:
--> find the value of 'x'
The function gives us a quadrilateral
--> separated into two triangles
In the triangle that has one angle with measure 65 degrees
-->it is an isosceles triangle thus the top most angle in that triangle is also
65 degrees
--> the other unknown angle is, therefore:
[tex]\text{unknown angle} + 65 + 65 = 180\\\text{unknown angle}+130=180\\\text{unknown angle}=180-130=50\\\text{unknown angle}=50[/tex]
Now that unknown angle forms a complementary relationship with the angle of the other triangle.
[tex]50 + \text{bottom most angle of other triangle}=90\\\text{bottom most angle of other triangle}=90-50\\\text{bottom most angle of other triangle}=40[/tex]
Now that the bottom triangle
--> has an angle with measure 'x'
--> that triangle is also an isosceles
--> meaning that our triangle's angle looks like this
[tex]40 + x+x+180\\2x+40=180\\2x=140\\x=70[/tex]
Answer: 70
Divides trapezoid abcd into two similar triangles, △abc and △acd. find the perimeter of this trapezoid if leg ab = 9 cm and leg cd = 12 cm.
If leg ab = 9 cm and leg cd = 12 cm then the perimeter of this trapezoid will be 46cm.
Angle bisector in geometry refers to a line that splits an angle into two equal angles. Bisector means the thing that bisects a shape or an object into two equal parts. If we draw a ray that bisects an angle into two equal parts of the same measure, then it is called an angle bisector.
Step-by-step explanation:
It is given that the angle bisector AC divides the trapezoid ABCD into two similar triangles Δ ABC and Δ ACD.
Let us first find the corresponding sides of triangles Δ ABC and Δ ACD.
Since AC is the angle bisector of ∠A,
∠DAC = ∠CAB --- (1)
Also, since ∠DAC and ∠ACB are alternate interior angles,
∠DAC = ∠ACB --- (2)
From (1) and (2),
∠CAB = ∠ACB
Therefore, in Δ ABC,
BC = AB (sides opposite to equal angles are equal)
So, BC = 9 cm.
Now, since ∠DAC = ∠ACB and ∠DAC = ∠CAB, we can take either ∠ACB or ∠CAB as the angle corresponding to ∠DAC. Let us take ∠ACB as the corresponding angle of ∠DAC.
So, the side opposite to ∠DAC in Δ ACD is the corresponding side to the side opposite to ∠ACB in Δ ABC.
That is, the side CD in Δ ACD is the corresponding side to the side AB in Δ ABC.
Now, suppose if the side BC in Δ ABC corresponds to side AD of Δ ACD, then the remaining side AC of Δ ABC should correspond to side AC of Δ ACD which is not possible since they are congruent.
So, the side BC in Δ ABC should correspond to side AC of Δ ACD and the remaining side AC of Δ ABC should correspond to side AD of Δ ACD.
Therefore, we have,
[tex]\frac{AB}{CD} =\frac{BC}{AC} =\frac{AC}{AD}[/tex]
But, [tex]\frac{AB}{CD} =\frac{9}{12} =\frac{3}{4}[/tex]
Therefore,[tex]\frac{BC}{AC} =\frac{3}{4}[/tex]
[tex]\frac{9}{AC} =\frac{3}{4}[/tex]
[tex]AC=(\frac{4}{3} )(9)[/tex]
AC = 12 cm
Also,
[tex]\frac{AC}{AD} =\frac{3}{4}[/tex]
[tex]\frac{12}{AD} =\frac{3}{4}\\AD=(\frac{4}{3} )(12)[/tex]
AD = 16 cm
Now, the perimeter of the trapezoid = AB + BC + CD + AD
= 9 + 9 + 12 + 16
= 46 cm
Therefore, the perimeter of this trapezoid will be 46cm.
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The perimeter of this trapezoid will be 46cm.
Now, According to the question:
Angle bisector in geometry refers to a line that splits an angle into two equal angles. Bisector means the thing that bisects a shape or an object into two equal parts. If we draw a ray that bisects an angle into two equal parts of the same measure, then it is called an angle bisector.
An angle bisector AC divides a trapezoid ABCD into two similar triangles △ABC and △ACD.
The leg AB=9 cm and the leg CD=12 cm.
Given that AC is the angle bisector of angle A, therefore:
∠DAC = ∠CAB ----- (1)
∠DAC = ∠ ACB (alternate interior angles) ---- (2)
From (1) and (2):
Sides opposite to equal angles are equal, therefore:
BC = AB
Hence, BC = 9 cm
Side BC in triangle ABC should correspond to side AC of triangle ACD and the remaining side AC of triangle ABC should correspond to side AD of triangle ACD.
Therefore, we have
[tex]\frac{AB}{CD} = \frac{BC}{AC} =\frac{AC}{AD}[/tex]
[tex]\frac{AB}{CD}[/tex] = [tex]\frac{9}{12}=\frac{3}{4}[/tex]
Therefore, [tex]\frac{BC}{AC}=\frac{3}{4}[/tex]
[tex]\frac{9}{AC}=\frac{3}{4}[/tex]
AC = 4/3 × 9
AC = 12cm
also, [tex]\frac{AC}{AD} =\frac{3}{4}[/tex]
12/AD = 3/4
AD = 4/3 ×12
AD = 16cm
Now, the perimeter of the trapezoid = AB + BC + CD + AD
= 9 + 9 + 12 + 16
= 46 cm
Therefore, the perimeter of this trapezoid will be 46cm.
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The complete question is this:
An angle bisector AC divides a trapezoid ABCD into two similar triangles △ABC and △ACD. Find the perimeter of this trapezoid if the leg AB=9 cm and the leg CD=12 cm.
Jayden bought some silver coins for x dollars. later, jayden sold the coins for 0.95x dollars. which describes the change in the price of the coins? a. 0.95% increase b. 95% increase c. 95% decrease d. 5% decrease
Answer:
d. 5% decrease
Step-by-step explanation:
You want the change in price of coins bought for x dollars and sold for 0.95x dollars.
ChangeThe percent change in price is given by ...
% change = ((new price)/(old price) -1) × 100%
% change = (0.95x/x -1) × 100% = (0.95 -1) × 100%
% change = -0.05 × 100% = -5%
The change in the price of the coins is described as a 5% decrease.
<95141404393>
What is the range of the function represented by the graph?
-2
474
2
-2
2
O {0, 1, 2, 3}
O {1, 2, 3, 4)
O 1sy≤4
O 0≤x≤3
The range of the function represented by the graph is 1 ≤ y ≤4. The correct option is c.
What is a graph?These visual representations include tables and graphs. They are employed to arrange data in order to highlight patterns and correlations. This information is displayed as a shape on a graph.
To present the results of their research, scientists and researchers frequently employ tables and graphs. Graphs present information to you as a picture or visual representation. This knowledge is referred to as "data." When you put data into a picture, it can appear lean or bulky, lengthy or short.
Therefore, the correct option is c, 1 ≤ y ≤4.
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4 yards to 30 inches
The ratio of the given conversion units is; 24:5
How to carry out unit conversion?Conversion of units is defined as the conversion between different units of measurement for the same quantity, and this is typically done through multiplicative conversion factors that change the measured quantity value without changing its effects.
Now, we are given a ratio of yards to inches but to get an effective ratio without units, we need to convert them to the same units.
Now, from conversion of units, we know that;
1 yard = 36 inches
Thus;
4 yards = 4 * 36 = 144 inches.
Thus;
The ratio = 144:30
This can be simplified to 24:5
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Find the product and express your answer in scientific notation.
(5 x 10^6)(8.2 x 10^-9)
The product of [tex]$ (5 \times 10^6)(8.2 \times10^{-9})[/tex] is [tex]$ 4.1 \times 10^{-2}[/tex] in scientific notation.
What is scientific notation?Numbers that are either too large or too small to be conveniently written in decimal form can be expressed using scientific notation. It is also known as "scientific form" in Britain, and it is frequently used by scientists, mathematicians, and engineers for difficult calculations involving large numbers. It is commonly referred to as "SCI" display mode on scientific calculators.
Scientific notation is a way to express numbers in terms of a decimal number between 1 and 10, but not 10 itself multiplied by a power of 10.
The standard for scientific notation is N × 10ᵃ
Given to find product of
⇒ [tex]$ (5 \times 10^6)(8.2 \times10^{-9})[/tex]
⇒ [tex]$ (5 \times 8.2 )10^{6 +(-9)}[/tex]
⇒ [tex]$ (5 \times 8.2 )10^{-3}[/tex]
⇒ [tex]$ (41 )10^{-3}[/tex]
⇒ [tex]$ 4.1 \times 10^{-2}[/tex]
Thus, The product of [tex]$ (5 \times 10^6)(8.2 \times10^{-9})[/tex] is [tex]$ 4.1 \times 10^{-2}[/tex] in scientific notation.
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12. There are 28 students whose last names begin with the letters G, H, J, or K. Information about
the probability of randomly selecting one of these students is listed below.
• probability of selecting a student whose last name begins with G: 1/7
•probability of selecting a student whose last name begins with G or H: 5/14
How many of these students have a last name that begins with H?
A. 4
B. 5
C. 6
D. 7
Answer:
6 (c)
Hope this helps
You are traveling from Minneapolis (3, 19) to Denver (-9, 11). You want to stop at a rest stop at exactly halfway. What are the coordinates of the halfway point?
The coordinate (x, y) of the midpoint is (2, 15)
What is Midpoint of a LineThe midpoint of a line is a point halfway between the two endpoints of the line, such that the line is divided into two equal segments. The coordinates of the midpoint can be found by taking the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints.
The formula of midpoint of a line is given as;
M = [(x₂ + x₁) / 2], [(y₂ + y₁) / 2]
The coordinates given are;
A = (3, 19)B = (-9, 11)M = [(-9 + 3) / 2], [(11 + 19) / 2]
M = (6/3) , (30/2)
M = 2, 15
The midpoint is (2, 15)
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What is the value of a?
Answer:
Step-by-step explanation:
What is secant example?
A secant is a straight line that intersects a curve at two points.
For example, consider the curve y = x^2. If we draw a secant line through the points (1,1) and (3,9), the secant line will intersect the curve at those two points.
Secants are often used to approximate the slope of a curve at a particular point. For example, if you want to find the slope of the tangent line to a curve at a point x = a, you can draw a secant line through that point and another point nearby, and use the slope of the secant line to approximate the slope of the tangent line.
To find the slope of the tangent line using a secant line, you can use the following formula:
Slope of tangent line = (y2 - y1)/(x2 - x1)where (x1, y1) and (x2, y2) are points on the secant line.
By taking the limit of this formula as x2 approaches x1, we can find the slope of the tangent line at the point where x = x1. This is known as the limit definition of the derivative.
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Type the correct answer in the box. determine the value of x in this polygon. a quadrilateral with one parallel side has interior angles labeled as follows. left parenthesis 6 x plus 3 right parenthesis degrees, left parenthesis2 x plus 8 right parenthesis degrees, and left parenthesis x plus 12.5 right parenthesis degrees. x =
The provided polygon is a quadrilateral, and by solving it, we discovered that x is, [tex]x = 23.5^\circ[/tex]
Used the concept of angle as a quadrilateral,
The total of the angles on two adjacent sides equals 180° when there are two additional angles on the same side.
Given that,
A polygon is shown in the image.
Now from the property of the quadrilateral, the equation is,
[tex](6x+3)^\circ + (x + 12.5)^\circ = 180^\circ[/tex]
[tex]7x + 15.5 = 180[/tex]
Subtract 15.5 on both sides,
[tex]7x= 164.5[/tex]
Divide 7 on both sides,
[tex]x= 23.5^ \circ[/tex]
Therefore, the value of x is 23.5°.
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2. Classify the pair of angles.
30⁰
30⁰
O adjacent
O complementary
O supplementary
none of these
(1 point)
The pair of angles 30⁰ and 30⁰ are supplementary angles.
Examples of additional angles
Angles with a supplementary sum are those whose sum is 180 degrees. For instance, the sum of angle 130° and angle 50° is 180°, hence they are supplementary angles. In the same way, complimentary angles sum to 90 degrees.
Supplementary angles may have three angles.
Three angles can't be added together. Two angles whose sum of the measures is exactly 180 degrees are supplementary angles, according to the definition. Even if three angles, such as 60 degrees, 30 degrees, and 90 degrees, sum up to 180 degrees, they would not be referred to as supplementary angles.
Supplementary angles add up to 180 degrees. An angle is supplementary to another angle if the sum of the measures of the two angles is 180 degrees. So, 30 + 30 = 60 which is supplementary.
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1. What is the standard deviation, a, in the heights of tenth grade girls shown in the table below? 01.2076 O≈ 1.4076 O~1.5076 O~1:3076 Heights of Girls (Inches) 64.25 65.50 63.75 64.25 66.50 62.75
Answer:
First option:
1.2076
Step-by-step explanation:
Just use the standard deviation functionality of any scientific/statistical calculator.
The answer is 1.2076 which is the first option
HELP
Write an equation of the line passing through point P that is parallel to the given line.
P(0,4);y=2x
Answer:
y = 2x +4
Step-by-step explanation:
You want an equation of the line through point P(0, 4) parallel to y = 2x.
Parallel lineThe parallel line will have the same slope, so can be written in the form ...
y = 2x +b
where 'b' is the y-intercept.
InterceptThe point (0, 4) is the y-intercept, telling you b=4.
An equation for the line is y = 2x +4.
__
Additional comment
"An equation" covers a lot of territory. The equation we found can be written several other ways, including ...
y - 2x - 4 = 02x -y = -4 . . . . . . . . standard form2x -y +4 = 0 . . . . . . general formx/(-2) +y/(4) = 1 . . . . intercept formy -4 = 2x . . . . . . . . . point-slope form<95141404393>
Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets for $15. The venue has the capacity to hold 300 people. The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise $3,500 for her school: Graph with x axis labeled pre sale tickets and y axis labeled at the door tickets. There are two lines intersecting at two hundred comma one hundred. How many pre-sale tickets must she sell to make her goal? 350 300 200 100
The number of pre-sale tickets must she sell to make her goal is (c) 200
How to determine the number of pre-sale tickets must she sell to make her goal?From the question, we have the following parameters that can be used in our computation:
Pre-sale tickets = $10 At-the-door tickets = $15. Capacity = 300 peopleAmount raised = $3,500These parameters can be represented using the following system of equations
10x + 15y = 3500
x + y = 300
The graph that completes the question is added as an attachment
From the graph, we have
(x, y) = (200, 100)
The variable y represents the number of pre-sale ticket
So, we have
x = 200
Hence, the number of pre-sale ticket is (c) 200
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Answer:
C, 200
Step-by-step explanation:
An easier way to get the answer in this case would be to see where the 2 lines meet, which is at 200 pre-sale tickets :))
How do you teach angles to 5th graders?
Teaching angles to 5th graders can be a fun and engaging process.
Here are a few strategies that you can use to help students understand angles:
Use visual aids: Diagrams and pictures are a great way to help students visualize angles. You can use protractors to measure angles and use pictures of real-world objects, such as a clock or a door, to help students see how angles are used in everyday life.Introduce the vocabulary: Make sure students understand the basic vocabulary associated with angles, such as right angle, acute angle, obtuse angle, and straight angle.Hands-on activities: Students learn best when they are actively engaged in the learning process. Hands-on activities, such as using a protractor to measure angles or using construction paper to create angles, can help students understand the concept of angles in a more concrete way.Games and puzzles: Games and puzzles are a great way to make learning about angles more fun. You can use games such as "Angry Birds" or "GeoGebra" to teach angle measurement and properties.Learn more about angles to 5th graders here: https://brainly.com/question/27781685
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Which point is a solution to the inequality 2x - у < 10?
The point that is a solution to the inequality 2x - у < 10 is (2, -5)
How to determine the point on the solutionFrom the question, we have the following parameters that can be used in our computation:
2x - y < 10
Next, we make the variable y the subject of the formula
Using the above as a guide, we have the following:
-y < 10 - 2x
Divide both sides by -1
y > 2x - 10
Assume a value for x
y > 2 * 2 - 10
So, we have
y > -6
This means that the possible y value at x = 2 is -5
Hence, the point is (2, -5)
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Can someone help me I missed like 3 weeks of school and didn’t learn this
In other words,
9 goes in the first box7 in the second box3 in the third box.=====================================================
Explanation:
Factor 63 and 27 such that the GCF 9 is involved.
63 = 9*727 = 9*3So,
63 - 27 = 9*7 - 9*3 = 9(7 - 3)
I used the distributive rule.
please help asap!!!
Thank you
Considering the figure the height of the tree is calculated to be 97.7 feet
How to find the height of the treeThe height of the tree is calculated using the trigonometry relation having the pneumonic SOH CAH TOA this is a short form for
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The image describes a right angle triangle of
opposite = height of the tree
adjacent = distance from the tree
The bearing is calculated using tan, TOA
tan 60 = h / WX
h = WX tan 60
Also, tan 40 = h / (60 + WX)
h = (60 + WX) tan 40
hence, equating both h
WX tan 60 = (60 + WX) tan 40
WX tan 60 = 60 tan 40 + WX tan 40
make WX the subject of the formula
WX tan 60 - WX tan 40 = 60 tan 40
WX (tan 60 - tan 40) = 60 tan 40
WX = 60 tan 40 / (tan 60 - tan 40)
substituting WX to h = WX tan 60
h = (60 tan 40 / (tan 60 - tan 40) ) * tan 60
h = 97.6557 feet
h = 97.7 feet to the nearest tenth
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solve for x 6.2= x - 11.8
Answer:
x = 18
Step-by-step explanation:
Solve for x:
6.2 = x - 11.8
6.2 = x - 11.8 is equivalent to x - 11.8 = 6.2:
x - 11.8 = 6.2
Add 11.8 to both sides:
x + (-11.8 + 11.8) = 11.8 + 6.2
11.8 - 11.8 = 0:
x = 6.2 + 11.8
6.2 + 11.8 = 18:
Answer: x = 18
Answer:
x-11.8=6.2
Step-by-step explanation:
add 11.8 for both sides
then x=11.8+6.2
the result of adding is 18
x=18.0
S.S={18.0}
Ashley is comparing banks she has 1,055 to put into a savings account.Bank #1 offers her an annual interest rate of 4.6% while bank #2 offers her a monthly interest rate of 0.3%.If she leaves the money in the account for 2 years,which bank will she earn more interest with?
In the 7th year, Marco will get compounded interest greater than $5, so he will have to keep money in the bank without withdrawing for 6 years.
Which bank will she earn more interest with?Simple Interest: is the interest based on the principal amount.
Compound Interest: is the interest based on the principal amount and the interest that accumulates on it every year.
So 5% simple interest on $100 = *100 =$5
So the compound interest needs to be greater than $5 .
Lets calculate the compound interest over the years.
1st Year: *100 =$4
2nd Year: Now to calculate the interest in second year the interest in first year will be accumulated. So interest will be calculated on 100 +4 =$104
4/100*104 =$4.16
3rd Year: Again interest from 2nd year will be added
4/100*108.16 =$4.33
4th Year: Again interest from 3rd year will be added
4/100*112.49 =$4.49
5th Year:
4/400*116.99 =$4.68
6th Year:
*121.67 =$4.87
7th Year:
*126.54 =$5.06
In the 7th year, Marco will get compounded interest greater than $5, so he will have to keep money in the bank without withdrawing for 6 years.
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Rationalize the denominator and simplify. √(a+1)-2 / √(a+1)+2
Answer:
[tex]\dfrac{a-4\sqrt{a+1}+5}{a-3}[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{\sqrt{a+1}-2}{\sqrt{a+1}+2}[/tex]
To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.
The conjugate of a binomial is where we change the sign between the two terms of the binomial. So the conjugate of √(a+1)+2 is √(a+1)-2.
Therefore:
[tex]\implies \dfrac{\sqrt{a+1}-2}{\sqrt{a+1}+2} \cdot \dfrac{\sqrt{a+1}-2}{\sqrt{a+1}-2}[/tex]
[tex]\implies \dfrac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)}[/tex]
[tex]\implies \dfrac{(a+1)-4\sqrt{a+1}+4}{(a+1)-4}[/tex]
[tex]\implies \dfrac{a-4\sqrt{a+1}+5}{a-3}[/tex]
12. On a 50-mile car trip back from the city, you must take a detour and drive the first twenty miles at 40 miles per hour. You only have 20 minutes to make it to post, so how fast will you have to drive
In the given situation we have to drive at the speed of 75 miles per hour.
What do we mean by speed?The speed at which an object's location changes in any direction.
The distance traveled in relation to the time it took to travel that distance is how speed is defined.
Since speed simply has a direction and no magnitude, it is a scalar quantity.
The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time.
So, we know that:
We must drive the first 25 miles at 40 miles per hour.
We have a time of 20 minutes.
20 minutes = 1/3 hour
Then our speed will be:
25 ÷ (1/3)
25 * 3/1
75 miles per hour
Therefore, in the given situation we have to drive at the speed of 75 miles per hour.
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Which data set could be represented by this box plot?
The data set that could be represented by the box plot would be = 32,36,27,30,35,39,28,34. That is option D.
What is a box plot?The box plot is defined as the type of data representation that is used in descriptive statistics to show the distribution of numerical data such as the number of hours Judy takes to complete a quilt.
The characteristics of the box plot is that is shows the outliers, the median, and the mode of the given numerical data.
Therefore, the data set that could be represented by the box plot would be = 32,36,27,30,35,39,28,34.
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Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
The total number of questions is 10 + 15 = 25.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points. The total number of points can be calculated by the following formula: x*5 + y*2.
For example, if there are 10 questions worth 5 points and 15 questions worth 2 points, the total number of points is calculated by 10*5 + 15*2 = 100.
In order to calculate the average points per question, we divide the total number of points by the total number of questions. This can be formulated as (x*5 + y*2) / (x + y).
For the example above, the average points per question can be calculated as (10*5 + 15*2) / (10 + 15) = 100 / 25 = 4. This means that the average points per question is 4 points.
Finally, if we want to calculate the total number of questions, we can use the formula x + y. Continuing with the example, the total number of questions is 10 + 15 = 25.
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14 questions worth 5 points and 15 questions worth 2 points
In this question we have been given that Mr. Martin’s math test worth 100 points, has 29 questions and each problem is worth either 5 points or 2 points.
We have been given a system of equations:
x + y = 29 ................(1)
5x + 2y = 100 ................(2)
Assuming x be the number of questions worth 5 points and let y be the number of questions worth 2 points, we need to find the number of questions of each point value.
i.e., we need to find the value of x and y
From equation (1),
x = 29 - y ..............(3)
Subatitute above value of x in equation (2)
5(29 - y) + 2y = 100
145 - 5y + 2y = 100
-3y = 100 - 145
-3y = -45
y = 15
Subatitute above value of y in equation (3)
x = 29 - 15
x = 14
Therefore, there are 14 and 15 questions worth 5 and 2, respectively.
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2(3a-2)+4a can some one please help me on this need step by step
Answer:
[tex]10a-4[/tex]
Step-by-step explanation:
[tex]2(3a-2)+4a=(6a-4)+4a=10a-4[/tex]
five hundred values are normally distributed with a mean of 125 and a standard deviation of 10 approximately how many values are within 2 standard deviations of the mean
68.27% of values are within 2 standard deviations of the mean.
What is normal distribution?Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Given that, five hundred values are normally distributed with a mean of 125 and a standard deviation of 10 approximately.
Here, X=125 and σ=10
The percent of the values lies between the interval 115-135 is calculated as follows;
P(115<X<135)=P(115-125/10 < X-μ/σ <135-125/10)
= P(-1<Z<1)
= 0.6827 (Obtained from the standard normal distribution table)
Therefore, 68.27% of values are within 2 standard deviations of the mean.
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What is 130% of 139.7
Answer: 181.61
Step-by-step explanation:
130 x 139.7
---------------- =181.61
100
Fitness universe has a membership fee of $50, after which individual visits to the gym are $5.50. Nonmembers pay eight dollars per visit. Stewart is going to exercise at the gym regularly, and is wondering whether it makes sense to become a member. How regularly when Stewart need to visit the gym, in order for a membership to be worth it?
For a membership to be worth it to Stewart, the number of days he will have to go to the gym would be 20 days
How to find the number of days to go to gym?Assuming the number of days that would make the gym membership worth it is x, the formula for finding the total cost of gyming with the membership fee is:
= 50 + 5. 50 x
The number of days as a nonmember would be:
= 8 x
The number of days till the membership is worth it is therefore:
8x = 50 + 5.50 x
8x - 5.50 x = 50
2. 50x = 50
x = 50 / 2. 50
x = 20 days
Stewart has to for for at least 20 days
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