Step-by-step explanation:
X-intercept is where the line crosses the x-axis or where y = 0
So, put y = 0 in the given equation
4x + 2(0) = 12
4x = 12
x = 12/4
x = 3
The first lawn is 7 meters long and 4 meters wide. the second lawn has the same length and width which is 3 times as much as the first one. what is the total area of the two lawns?
The area of the two lawns will be 105 square meters.
According to the question,
We have the following information:
The first lawn is 7 meters long and 4 meters wide. The second lawn has the same length and width which is 3 times as much as the first one.
So, the width of the second lawn = 4×3
Width of second lawn = 12 m
Now, the formula to find the area of the rectangle:
Length*width
Area of first lawn:
7×3
21 square meters
Area of second lawn:
7×12
84 square meters
Now, the area of two lawns = area of first lawn+ area of second lawn
Area = 21+84
Area = 105 square meters
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Help Help Pls Begging Brainliest!!!!!!!!!!!!!!!!
Our school flag is a rectangle. We are changing to a new rectangular flag design. The length of the new flag is 20% greater than the length of the old flag, and the width of the new flag is 10% less than the width of the old flag, The old school flag is 25 square feet. What is the area of the new flag?
Answer:
27 square feet-------------------------------
Let the sides of the old rectangle are l and w.
Its area isA = lw = 25New flag has dimensionsLength is 20% greater = 1.2lWidth is 10% less = 0.9wArea of new flagA = 1.2l × 0.9w = 1.08 lwA = 1.08×25 = 27Answer: Hence the answer is 27 square feet.
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on a particular stretch of highway, the state police know that the average speed is 62 mph with a standard deviation of 5 mph. on a busy holiday weekend, the police are concerned that people travel too fast. so they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. let's assume, for the moment, that people travel at the same speed on holiday weekends as they typically do on other days. calculate the mean and standard deviation of the sampling distribution of sample means for samples of size n
The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.
What is a standard deviation?
Data dispersion in regard to the mean is quantified by a standard deviation. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Here, we have
µ = 62 , σ = 5
P ( X < 66 )
By applying the standard deviation formula, we get
Z = ( X - µ ) / (σ/√(n)
Z = ( 66 - 62 ) / ( 5 / √50 )
Z = 5.6569
P ( ( X - µ ) / ( σ/√(n)) < ( 66 - 62 ) / ( 5 / √(50) )
P ( X < 66 ) = P ( Z < 5.66 )
P ( X < 66 ) = 1
P ( X > 66 ) = 1 - P ( X < 66 )
By applying the standard deviation formula, we get
Z = ( X - µ ) / ( σ / √(n))
Z = ( 66 - 62 ) / ( 5 / √ ( 50 ) )
Z = 5.6569
P ( ( X - µ ) / ( σ / √ (n)) > ( 66 - 62 ) / ( 5 / √(50) )
P ( Z > 5.66 )
P ( X > 66 ) = 1 - P ( Z < 5.66 )
P ( X> 66 ) = 1 - 1
P ( X> 66 ) = 0
Hence, the probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.
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(1 point) the radius of a right circular cone is increasing at a rate of 5 inches per second and its height is decreasing at a rate of 3 inches per second. at what rate is the volume of the cone changing when the radius is 20 inches and the height is 40 inches?
The rate of change of volume is 418.6 inch³/s .
Rate of increase of radius with time is ( dr/dt ) = 5
rate of decrease of height with time is (dh/dt ) = -3
volume of a cone is given by (V) = [tex]\frac{1}{3} \pi r^{2}h[/tex]
Now the rate of change of volume with respect to time is given by dV/dt
∴ dV/dt = d( [tex]\frac{1}{3} \pi r^{2}h[/tex]) / dt
dV/dt = [tex]\frac{1}{3} \pi (2rh\frac{dr}{dt} + r^{2}\frac{dh}{dt} )[/tex]
value of radius and height when volume is changing are :
r = 20 inches
h = 40 inches
dV/dt = [tex]\frac{1}{3} \pi ([/tex] 2×20×40 ×5 - [tex]20^{2}[/tex]×3 )
dV/dt = [tex]\frac{1}{3} \pi[/tex](1600 - 1200)
dV/dt = (400/3) 3.14
dV/dt = 418.66 inch³/s
So the rate of change of the volume is 418.66 inch³/s.
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a simple random sample is group of answer choices a sample that gives every possible sample of the same size from the same population the same chance to be selected. a sample that selects equal numbers of individuals from each stratum. any sample that gives every individual the same chance to be selected. a sample that contains the same percent of each subgroup in the population. any sample that is selected without replacement.
It is also called as Random Sample experiment.
What is random sample experiment?Random assignment is a technique used in experimental research to divide individuals from your sample into several groups using randomness.With this approach, each sample participant has a known or equal chance of being assigned to either the experimental group or the control group.In an experiment, random assignment and random selection are both possible. Imagine that 500 people are randomly chosen from a population to take part in your study.A subset of a statistical population called a simple random sample is one in which each member has an equal chance of being chosen. A straightforward random sample is intended to be an objective depiction of a group.Hence, it is an random experiment.
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a tire manufacturer wishes to investigate the tread life of its tires. a sample of 10 tires driven 50,000 miles revealed a sample mean of 0.32 inches of tread remaining with a sample standard deviation of 0.09 inches. construct a 95% confidence interval for the population mean.
The confidence interval for the population mean is 0.2896 , 0.3505)
The sample mean is x = 0.32
The sample standard deviation is s = 0.09
The sample size is n = 10
The population standard deviation is unknown and sample size is atleast 10.
Thus use the t distribution.
Replacing the values in the following formula, determine the 95% confidence interval.
95% C.I = x ± t₀.₉₅,ₙ₋₁ . Sm
= x ± t₀.₀₅/₂,₁₀₋₁ . s/√n
= 0.32 ± 2.03 . 0.09/√10
= (0.2896 , 0.3505)
Hence the confidence interval for the population mean is 0.2896 , 0.3505)
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Can you please help me in this question.
Answer:
Don't know if i did it right but i think it is:
a=14
b=6
c=5
The measure of x is.
Answer:
Step-by-step explanation:
Ok:
1. Caculate all of the two triangles' angles
First triangle on the left!
50+90= 140+40= 180degrees
So: Angles for first one are 50,90,40
Second Triangle on right
51+90= 141+39= 180degrees
So: Angles for second one are 51,90, 39
2. Subtract the corners added together from 180 degrees
40+39= 79 degrees
180-79=101 degrees
3. Answer: Choice B or 101 degrees!
the two scatterplots below show the relationship between final and mid-semester exam grades recorded during several years for a statistics course at a university. (a) based on these graphs, which of the two exams has the strongest correlation with the final exam grade? explain. (b) can you think of a reason why the correlation between the exam you chose in part (a) and the final exam is higher?
a) Exam 2 has the strongest correlation with the exam grade, according to the graphs below. Since the points are arranged in a positive band that extends from bottom left to upper right.
b) Because there is a positive association and there is little dispersion of points, the correlation between exams and the final exam is higher.
Define correlation.The link between variables is described by correlation. It can be characterized as strong or weak, as well as positively or negatively.
Given,
The two scatterplots below show the relationship between final and mid-semester exam grades recorded during several years for a statistics course at a university.
a) Exam 2 has the strongest correlation with the exam grade, according to the graphs below. Since the points are arranged in a positive band that extends from bottom left to upper right.
b) Because there is a positive association and there is little dispersion of points, the correlation between exams and the final exam is higher.
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ester Sarai and kurry each chose a number esters number is 1/10 of saris kurrys number is 10 times as much as sarais sarais number is 0.09. what number did each person choose?
The number ester,sarai and kurry chose are 0.009,0.09 and 0.9 respectively
What is Multiplication?Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. For example 3+3+3+3+3 can be written as 3× 5 .
to find the ester's number= 1/10 of sarai's number
= 1/10× 0.09
= 0.009
to find kurry^s number = 10 × sarai's number
= 10× 0.09
= 0.9
Therefore ester , sarai and kurry chose 0.009, 0.09,0.9 respectively.
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In the figure below, lines m and n are parallel.
What is the value of x?
OA. 30
B. 35
OC. 45
OD. 40
m-
n+
(4x + 5)°
xo
Answer:
B. 35
Step-by-step explanation:
Because lines m and n are parallel, we know that x+(4x+5)=180.
So all you have to do is simplify.
x+(4x+5)=180
5x+5=180
5x=175
x=35
So the only possible value of x is 35
PLEASE HELP WHAT IS THE SLOPE OF THIS LINE
Answer: A. [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
To find the slope we must find the change in y over the change in x. Δ
Or rise over run. [tex]\frac{rise}{run}[/tex]
In the graph, we have two "good" points. (0, -6) and (4,0)
So for Δy 0 to -6 = -6
So -6 goes on top [tex]\frac{-6}{x}[/tex]
Now Δx goes from 4 to 0 so the change would be -4.
So now it becomes [tex]\frac{-6}{-4}[/tex]
Since there are two negatives it becomes a positive. [tex]\frac{6}{4}[/tex] Or simply put, [tex]\frac{3}{2}[/tex]
please help lol I need help
The expression can be expanded as 125/64
Evaluating an ExpressionTo evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
To solve this problem, we need to evaluate the expression given;
For this, we can find the cube of the numerator and cube of the denominator.
(5/4)³ = 125/64
The solution to the problem is 125/64
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y=3/4x−1/2 linear equation
The equation's graph is a straight line: y= 3/4x - 1/2.
What is a straight line?A straight line is a line with an infinite length and no curves. A straight line can also be drawn between any two places, but its endpoints must stretch into the infinite.When two places A (x1, y1) and B (x2, y2) are connected by the shortest path possible, and the line ends are stretched to infinity, a straight line is the result.acc to our question-
There are an endless number of solutions to a linear equation with two variables, and we can obtain each one as a pair of numbers.
Draw the two-variable linear equation's graph by plotting these values on a coordinate plane.
Using the slope and y-intercept is the simplest approach to graph something in slope-intercept form because that information is already available.
Follow all of the instructions listed below to plot the equation's graph.
Step 1: When x = 0, the y-intercept is 0, and y would then equal -1/2. (0, -1/2) are the points.
Step 2: Since the slope is 3/4 rise over run, go three up (rise) and four across (run).
Step 3: The slope of the line is upward since the slope in the equation, not negative.
Step4; There are two points, draw a line connecting the two points.
hence,The equation's graph is a straight line: y= 3/4x - 1/2.
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Which statement is logically equivalent to the following conditional statement?
"If it has exactly four sides, then it is not a hexagon."
O If it does not have exactly four sides, then it is not a hexagon.
O If it does not have exactly four sides, then it is a hexagon.
O If it is a hexagon, then it does not have exactly four sides.
O If it is not a hexagon, then it has exactly four sides.
The statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."
What is a regular hexagon?
It is a regular hexagon when the lengths of all the sides and the measures of all the angles are equal. In a regular hexagon, each inside angle is 120 degrees. The characteristics of a regular hexagon. The lengths of each side are equal.
Here, we let
P = it has exactly four sides.
Q = it is not an hexagon.
The negation is like this;
If it is a hexagon, then it does not have exactly four sides.
Thus, we concluded that “it is a hexagon” is your hypothesis (p) and “it has exactly 6 congruent sides” is your conclusion (q).
Hence, the statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."
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Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Hartford was $220. Now the cost is $355. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percentage increase is 61.36%. If the airline charges an additional $50 baggage fee, the new percentage increase will be 45.68%.
What is the percent increase?A percentage increase denotes how much a percentage has risen over time. To get at this figure, discover the difference between the original and final values, then deduct it to get the actual sum of the decrease.
The idea of Percentage increase is simply the amount of increase from the original(initial) to the final figure expressed in terms of 100 parts of the original. E.g. A 10% increase implies that if the original value is divided into 100 parts, the value has increased by an extra 10 parts. So, if the initial value rose by 16%, the value would rise by 16 for every 100 units, and so on.
The formula for calculating the percentage increase can be expressed as:
[tex]\%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]
[tex]\%\ increase= \frac{355- 220}{220}\times 100[/tex]
[tex]\%\ increase= \frac{135}{220}\times 100[/tex]
[tex]\mathbf{=61.36\%}[/tex]
[tex]New \ \%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]
[tex]New \ \%\ increase= \frac{405- 220}{405}\times 100[/tex]
[tex]New \ \%\ increase= \frac{185}{405}\times 100[/tex]
[tex]New \ \%\ increase=\mathbf{45.68\%}[/tex]
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Select all rational numbers.
√75
-√25
2*√7
√100
√0.36
√0.0144
√3/7
-√36/49
The rational numbers are -√25, -√25, √100, √0.36, √0.0144 and -√36/49. Select them
How to identify rational numbers?A rational number is a number that can be expressed as a fraction where both the numerator and the denominator in the fraction are integers e.g 2/3, 7/1, √100 = 10/1, etc.
An irrational number is any real number that cannot be expressed as the quotient of two integers. This is the opposite of rational numbers. They are usually of roots that cannot give integers e.g 3√5, √8, etc.
√75 = √(25 x 3) = √25 x √3 = 5 x √3 = 5√3 (This is not rational)
-√25 = -5 = -5/1 (This is rational)
2*√7 = 2√7 (This is not rational)
√100 = 10 = 10/1 (This is rational)
√0.36 = √(36/100) = 6/10 (This is rational)
√0.0144 = √(144/10000) = 12/100 (This is rational)
√3/7 = √3/7 (This is not rational)
-√36/49 = -6/7 (This is rational)
Therefore, -√25, -√25, √100, √0.36, √0.0144 and -√36/49 are rational numbers. They should be selected
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Drag each expression to show whether it is equivalent to 54x+18 or (6⋅9x) + (6⋅1).
The equivalent expression of the expression 54x + 18 will be 18(3x + 1). Then the correct option is E.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 54x + 18
Simplify the expression, then we have
⇒ 54x + 18
⇒ 18(3x + 1)
The equivalent expression of the expression 54x + 18 will be 18(3x + 1). Then the correct option is E.
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The complete question is given below.
Drag each expression to show whether it is equivalent to 54x + 18, 18(3x – 1), or (6 • 9x) + (6 • 1).
expressions: A-54x B-(6 • 9x) + (6 • 3) C-54x + 6 D-3(18x+2) E-18(3x+1) F-(9*6x)-(9*2)
T2 Midterm Re
1. X and Y are two fractions. X is greater than 0 but less than 1.
Which statement describes the product of X and Y?
A.
The product is less than -1.
B. The product is greater than -1 but less than 0.
C. The product is greater than 0 but less than 1.
D. The product is greater than 1.
Answer: The correct answer is C. The product is greater than 0 but less than 1.
Step-by-step explanation:
X and Y are both fractions
X is greater than 0 but less than 1
X * Y > 0 and < 1
The product of these two fractions will result in a fraction between 0 and 1.
For example:
1/2 x 1/2 =1/4, 1/6 x 2/6 = 1/18, 1/10 x 5/6 = 1/12
Show me how to graph this by using key points step by step please and I will give you brainliest!
g(x)=log(6-3x)+1
Answer:
136-5x
Step-by-step explanation:
What is 9 4/5+7 2/3 = ? as a mixed number
Answer:
42/4/5 first you divide 72➗ 3 then you get 24 then see the picture is you
Answer:
17 7/15
Step-by-step explanation:
Rewrite:
9 + 4/5 + 7 + 2/3
Add whole numbers:
9 + 7 = 16
Add fractions:
4/5 + 2/3 --> 12/15 + 10/15 = 22/15
Simplify:
22/15 --> 1 7/15
Add all components:
16 + 1 7/15 = 17 7/15
1. A recipe for salad dressing calls for three parts oil for every one part vinegar. How many tablespoons of vinegar are needed to make 1/2 cup of salad dressing?
Answer: The answer is 8
Step-by-step explanation: 16 tablespoon is 1 cup now find half of 16. Half of 16 is 8. So 8 tablespoon should be equal 1/2 cup
5/6 divided by
(- 13/7)
Roscoe is a professional groomer.
What is the unit rate for grooming per hour?
5 dogs per hour
15 dogs per hour
3 dogs per hour
1 dog per hour
the cost of a taxi ride consist of a flat fee plus a cost per mile. if 30 miles cost $20 and 50 miles cost $30, write a linear function that describes the cost of a trip, c, in terms of the number of miles, n. what is the cost per mile and what is the flat fee?
A linear function that describes the cost of a trip, c, in terms of the number of miles, n will be "c=0.60n+0.67n" and cost per mile is $0.6 and $0.67 and the flat fee is $50.
What is cost per mile?Once you are aware of your mileage and total expenses, calculating cost per mile becomes a straightforward equation. Your cost per mile is calculated by dividing your total expenses by the total number of miles you have driven. Your expenses per mile are influenced by your variable and fixed costs, so you should probably pay closer attention to how much you're shelling out for each mile your drivers cover. You can better understand your primary costs and produce more accurate bids for new contracts by knowing your expenses at this specific level.
Here,
cost per mile,
20/30=$0.67/mile
30/50=$0.60/mile
c=0.60n+0.67n
flat fee,
=$30+$20
=$50
The cost per mile is $0.6 and $0.67, and the flat rate is $50. A linear function that expresses the cost of a trip, c, in terms of the number of miles, n, will be "c=0.60n+0.67n".
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what sample size is necessary for a 90% confidence interval about the mean height of a shrub if we want a margin of error of 0.5 inches and the population standard deviation is known as 1.3 inches.
The sample size necessary for a 90% confidence interval about the mean height of a shrub with a margin of error of 0.5 inches and a population standard deviation of 1.3 inches is 18.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error = 0.5 inches
z = found by using a z-score table
SD = sample standard deviation = 1.3 inches
n = sample size
At 90% confidence interval, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.647
Plug in the values to the formula and solve for the sample size, n.
MOE = z x (SD / √n)
0.5 = 1.647 x (1.3 / √n)
√n = 1.647(1.3) / 0.5
n = 18.34
n = 18
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What the answer pls help The distance from the tip of a slice of pizza to the crust is 6 inches.
The measurement of the distance from the tip of the slice of pizza to the crust is the radius.
The diameter of the pizza is 12 inches and the circumference is 37.7 inches
How to find the circumference?A slice of pizza is cut from the middle of the pizza to the crust. It is therefore cut from the middle of the pizza (circle) to the edge of the pizza (circle).
This is the radius because the radius is the straight - line distance from the edge of the middle of a circle to the edge.
If the radius is 6 inches, the diameter is:
= radius x 2
= 6 x 2
= 12 inches
The circumference is:
= π x diameter
= 22/7 x 12
= 37.7 inches
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PLEASE HELP, NEED ASAP
Answer:
Step-by-step explanation:
In AWXY, WY is extended through point Y to point Z, m/Y W X = (3x + 17)°, m/XYZ = (10z - 5)°, andm/W XY = (3x + 2)°. Find m/W XY.
Using the exterior angle theorem, the measure of angle WXY is calculated as: 20°.
How to Apply the Exterior Angles Theorem?Given the triangle in the image below has the following:
The measure of exterior angle XYZ = (10x - 5)°The measure of remote angle WXY = (3x + 2)°The measure of remote angle YWX = (3x + 17)°According to the exterior angles theorem, the sum of the two remote angles would be equal to the measure of the exterior angles, therefore:
10x - 5 = 3x + 2 + 3x + 17
Combine like terms
10x - 5 = 6x + 19
10x - 6x = 5 + 19
4x = 24
4x/4 = 24/4
x = 6
m∠WXY = 3x + 2 = 3(6) + 2
m∠WXY = 18 + 2
m∠WXY = 20°
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A swimming pool is to be constructed in a 1,176-ft2 backyard. there is to be a fence that will surround a 14-by-28-foot pool. the pool builder wants to build a concrete paver deck of a uniform width, x, surrounding the pool and filling the entire area of the backyard. what is the width of the pool deck? 7 ft 14 ft 28 ft 56 ft
The width of pool deck is 7 ft and new dimensions of pool and deck are 21 ft and 35 ft .
In the given question we have,
Area of whole background ( pool + deck) = 1176 ft²------(1)
Area is a two dimensions quantity . so, we work here in 2-D.
length of pool = 28 ft , width of pool= 14 ft
let the width of deck be x ft . Now, the new dimensions are following
length of pool and deck = 28 + x + x = (28+2x ) ft
width of pool and deck = 14 + x + x = (14+ 2x) ft
here, 2x include in lenth and width for surronding deck.
total area of pool and deck ( backyard ) = lenth × width = 1176 ft² ( from (1) )
(28+2x) ( 14+2x) = 1176 ----(2)
Now, we shall solve above equation (2) and find out value of x
28×14 + 56x + 28x + 4x^2 = 1176
=> 4x²+ 84x + 392 - 1176 = 0
=> 4x² + 84x - 784=0 => x² + 21x - 196 = 0
=> x²+ 28x - 7x - 196 = 0 => x(x+ 28) - 7(x+28)=0
=> (x+28) (x-7) = 0
either x + 28= 0 or x - 7 = 0 =>either x= -28 or x= 7
but width can't be negative value so, discard
x= -28.
Hence, the width of pool deck is 7 ft.
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