Answer:
A. 15
Step-by-step explanation:
HI and IJ are both segments in the line HJ so HI and IJ combined equal the total length of HJ. This means we can write an equation using HI and IJ and setting them equal to HJ.
6x + 8 + 2x - 4 = 124
next step is to combine like terms:
8x + 4 = 124
then, subtract 4 from both sides.
8x + 4 = 124
-4 -4
8x = 120
finally, divide both sides by 8.
8x/8 = 120/8
x = 15
since it is equal to x, 15 is your solution!
A store has a 28% off sale on hammers. Before the discount, the price of a hammer is $49. What is the sale price?
If BE=9cm, find GE
What is the answer
Answer:
GE = 3 cm
Step-by-step explanation:
BE = 9 cm
Since G is the centroid, therefore:
\( GE = \frac{1}{3}(BE) \) => Centroid theorem
Plug in the value
\( GE = \frac{1}{3}(9) \)
GE = 3 cm
please help ASAP !
Please help ASAP !
Answer:
5/7
Step-by-step explanation:
4/7+1/7 is 5/7 and 5/7 is its simplest form. Hope this helps :)
Answer:
the answer is 5/7
Step-by-step explanation:
hope it helps:)
Josiah plants vegetable seeds in rows. Each row has the same number of seeds in it. He plants more than one row of seeds. What could be the total number of seeds he plants?
The total number of seeds that Josiah would plant would be = nR×S
How to determine the total number of seeds that Josiah will plant?To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.
Let each row be represented as = nR
Where n represents the number of rows planted by him.
Let the seed be represented as = S
The total number of seeds he planted = nR×S
Therefore, the total number of seeds that was planted Josiah would be = nR×S.
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In
1950
19501950, the per capita gross domestic product (GDP) of Australia was approximately
$
1800
$1800dollar sign, 1800. Each year afterwards, the per capita GDP increased by approximately
6.7
%
6.7%6, point, 7, percent.
Write a function that gives the approximate per capita GDP
G
(
t
)
G(t)G, left parenthesis, t, right parenthesis of Australia
t
tt years after
1950
19501950.
Do not enter commas in your answe
The function that approximates Australia's per capita GDP in t years after 1950 is \(G(t) =$1800(1.067)^t.\)
What is a Function?A function sets the value of one set's elements to the value of another set's specified element.
GDP represents the monetary worth of final products and services (those purchased by the final user) generated in a country over a certain time period.
According to the given information:
Given that Australia's GDP in 1950 was $1800, and that it is expanding by 6.7% per year, the GDP of Australia will increase by 6.7% each year after 1950.
As a result of the compounding effect, a function that gives the estimated per capita GDP of Australia in t years following 1950 can be expressed as follows:
\(GDP = 1800 + (1+6.7)^{t}\)
\(GDP = $1800 + (1+0.067)^t\)
\(GDP = $1800 + (1.067)^t\)
Hence, The function that approximates Australia's per capita GDP in t years after 1950 is \(G(t) =$1800(1.067)^t.\)
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Cassandra is hanging crystal stars from the gym ceiling using string for the homecoming dance. She wants the ends of the strings where the stars will be attached to be 7 feet from the floor. Use the diagram to determine how long she should make the strings
12/5 yards is the length she should use to make the string.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that Cassandra is hanging crystal stars from the gym ceiling using string for the homecoming dance
She wants the ends of the strings where the stars will be attached to be 7 feet from the floor.
BD is perpendicular to AC.
∠BDA+∠2+∠3=180
∠2+∠3=90 degrees.
∠1=∠3 (the equivalent substitution)
ΔABD=ΔBCD
AD/BD=BD/DC
(Similar triangles have sides that are proportional)
AD.DC=BD²
PC⊥AC
∠ACP=90 degrees.
∠ACM+∠MAC+∠∠CAM=180
∠ACM=∠APC
Therefore ΔAMC~ΔPCA
CM/CD=AC/AD
CM=12/5 yards
Hence, 12/5 yards is the length she should use to make the string.
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Answer: 18
Step-by-step explanation:
First, find x for x-2. So you would use one of the Geometric Mean Theorems using 5 and a height of 10. For this problem, we will use "y" as a placeholder for finding the whole total of that side.
\(\frac{5}{10} =\frac{10}{y} \\\) Solve. --> \(5y = 100\\\) --> \(\frac{5y}{5} =\frac{100}{5} \\\) --> y = 20
Then subtract 20 from 2 to find x. You get 18 as an answer.
A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed are supposed to contain 300m. In fact, the contents vary according to a Normal Distribution with mean of 298 mL and a standard deviation of 3 mL. (a) What is the probability that an individual bottle contains less than 295 mL? Show your work. (b) What is the probability that the mean contents of six randomly chosen bottles is less than 295 mL? Show your work.
Answer:
0.15866 ; 0.0071627
Step-by-step explanation:
Given that:
Mean (m) = 298
Standard deviation (s) = 3
A.) P(x < 295)
Using the relation to obtain the standardized score (Z) :
Z = (x - m) / s
Z = (295 - 298) / 3 = - 1
p(Z < - 1) = 0.15866 ( Z probability calculator)
B.)
Z = (x - m) / s /sqrt(n)
Z = (295 - 298) / 3/sqrt(6) = −2.449489
p(Z < - 2.449) = 0.0071627 ( Z probability calculator)
Given values are:
Mean,
m = 298Standard deviation,
s = 3(a)
P(x < 295)
The standardized score will be:
→ \(Z = \frac{(x-m)}{s}\)
By substituting the values, we get
\(= \frac{(295-298)}{3}\)
\(= \frac{-3}{3}\)
\(= -1\)
Now,
By using the Z probability calculator, we get
→ \(p(Z< -1) = 0.15866\)
(b)
The standardized score will be:
→ \(Z = \frac{x-m}{\frac{s}{\sqrt{n} } }\)
By putting the values,
\(= \frac{295-298}{\frac{3}{\sqrt{6} } }\)
\(= -2.449489\)
Now,
→ \(p(Z < -2.449)= 0.007163\)
Thus the responses above are correct.
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Otto is told the average low temperature in January is 16.1∘C cooler than the average low temperature in November. What equation can Otto use to find the average low temperature in January?
Answer:
x - 16.1°C
Step-by-step explanation:
Given that average low temperature in January is 16.1 cooler Than average low temperature in November
Let average low temperature in November = x
Since, average low temperature in January is cooler than average low temperature in November, then, January temperature is less Than in November
Hence,
Average low temperature in January :
[Average low temperature in November - 16.1°C]
(x - 16.1°C)
Question 10(Multiple Choice Worth 5 points)
(Identifying Functions LC)
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1
Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
Is the relation a function:
No, because for each input there is not exactly one output.How to know if the relation is a functionTo determine if the relation is a function, we need to check if there is exactly one output for each input.
Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).
This means that there are two outputs for the same input, so the relation is not a function.
Therefore, the correct answer is: "No, because for each input there is not exactly one output."
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how do you solve a problem like this:
5(4x-9)
Answer:20 x - 45
Step-by-step explanation: 5 multiply 4x = 20X
5 multiply 9 = 45
and the subtract sign is because it is the same sign on the brackets.
What is the slope of the line y=8?
Answer:
undefined or 0
Step-by-step explanation:
Answer:
The answer is 0 because undefined is straight up or vertical
there are two important properties of probabilities. 1) individual probabilities will always have values between and . 2) the sum of the probabilities of all individual outcomes must equal to .
1.) Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.
2.) The sum of probabilities of all possible outcomes is equal to 1.
1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.
A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.
Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.
2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.
Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.
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points a (-2,5) and b (1,-8) are placed in two different quadrants of a cartesian coordinate system. convert each set of cartesian coordinates to polar coordinates. the angle should be reported as a positive angle, in degrees, from the positive x-axis. (0° < θ < 360°)
The polar coordinates for point A (-2, 5) are
\((r, \theta) = (\sqrt{2^2 + 5^2}, \tan^{-1}\left(\frac{5}{-2}\right)) \\\\\approx (5.39, 112.62^\circ).\)
The polar coordinates for point B (1, -8) are
\((r, \theta) = (\sqrt{1^2 + (-8)^2}, \tan^{-1}\left(\frac{-8}{1}\right)) \\\\\approx (8.06, -81.87^\circ).\)
To convert cartesian coordinates to polar coordinates, we need to determine the distance from the origin (r) and the angle (θ) the point makes with the positive x-axis.
For point A (-2, 5):
1. Calculate the distance from the origin using the distance formula:
\(r = \sqrt{(-2)^2 + 5^2} \\\\= \sqrt{4 + 25} \\\\= \sqrt{29} \\\\\approx 5.39.\)
2. Calculate the angle θ using the arctangent function:
\(\theta = \tan^{-1}\left(\frac{5}{-2}\right) \\\\\approx 112.62^\circ.\)
For point B (1, -8):
1. Calculate the distance from the origin:
\(r = \sqrt{1^2 + (-8)^2} \\\\= \sqrt{1 + 64} \\\\= \sqrt{65} \\\\\approx 8.06."\)
2. Calculate the angle θ:
\(\theta = \tan^{-1}\left(\frac{-8}{1}\right) \\\\\approx -81.87^\circ.\)
Since the point is in a different quadrant, we report the angle as negative. To convert it to a positive angle, we can add 360°:
\(-81.87^\circ + 360^\circ \approx 278.13^\circ.\)
Thus, the polar coordinates for point A are approximately (5.39, 112.62°) and for point B are approximately (8.06, 278.13°).
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How are 198:1,287 and 2:13 equivalent ratios
Expressing 198 : 1287 in its simplest form, gives the value 2 :13 ; Hence, the two ratio expressions are equivalent.
In other to determine if 198:1,287 and 2:13 are equivalent ratios ;
Breakdown 198 : 1287 such that it is expressed in its lowest termIf the ratio obtained is equal to 2 : 13 ; then both ratio values are equivalent.Dividing both values by 99 ;
198 : 1287 = 2 : 13
Since, the ratio 198 : 1287 simplified to its lowest term equals 2 : 13 ; then both ratios are equivalent.
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find the volume of the given solid. bounded by the coordinate planes and the plane 6x + 4y + z = 24
Therefore, the volume of the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is 96 cubic units.
To find the volume of the solid bounded by the coordinate planes (xy-plane, xz-plane, and yz-plane) and the plane 6x + 4y + z = 24, we need to determine the region in space enclosed by these boundaries.
First, let's consider the plane equation 6x + 4y + z = 24. To find the x-intercept, we set y = 0 and z = 0:
6x + 4(0) + 0 = 24
6x = 24
x = 4
So, the plane intersects the x-axis at (4, 0, 0).
Similarly, to find the y-intercept, we set x = 0 and z = 0:
6(0) + 4y + 0 = 24
4y = 24
y = 6
So, the plane intersects the y-axis at (0, 6, 0).
To find the z-intercept, we set x = 0 and y = 0:
6(0) + 4(0) + z = 24
z = 24
So, the plane intersects the z-axis at (0, 0, 24).
We can visualize that the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is a tetrahedron with vertices at (4, 0, 0), (0, 6, 0), (0, 0, 24), and the origin (0, 0, 0).
To find the volume of this tetrahedron, we can use the formula:
Volume = (1/3) * base area * height
The base of the tetrahedron is a right triangle with sides of length 4 and 6. The area of this triangle is (1/2) * base * height = (1/2) * 4 * 6 = 12.
The height of the tetrahedron is the z-coordinate of the vertex (0, 0, 24), which is 24.
Plugging these values into the volume formula:
Volume = (1/3) * 12 * 24
= 96 cubic units
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Jayden’s family is going to Magic Mountain Amusement Park. It is 320 miles. They drive at an average speed of 64 miles per hour on highway. How long will it take Jayden’s family to get to the park?
The unknown quantity, equation, and the answer in a complete sentence.
Answer:
5 hours
Step-by-step explanation:
You can use a simple equation for this problem, speed times time is distance. s * t = x. In this case, the distance, x, is 320 and the speed, s, is 64. We can move the s from the equation around and get t = x/s. So time = 320/64 which is 5 hours.
ahhhhhhhhhhhhhhhhhhhhhhhh help plz
8 cups
I just know 8m good at math
PROBLEM SOLVING You are flying in a hot air balloon about 1.2 miles above the ground. Find the measure of the arc that
represents the part of Earth you can see. Round your answer to the nearest tenth. (The radius of Earth is about 4000 miles)
4001.2 mi
Z
W
Y
4000 mi
Not drawn to scale
The arc measures about __
The arc degree representing the portion of Soil you'll see from the hot air balloon is around 0.0 degrees.
How to Solve the Arc Degree?To discover the degree of the arc that represents the portion of Earth you'll be able to see from the hot air balloon, you'll be able utilize the concept of trigonometry.
To begin with, we got to discover the point shaped at the center of the Soil by drawing lines from the center of the Soil to the two endpoints of the circular segment. This point will be the central point of the bend.
The tallness of the hot discuss swell over the ground shapes a right triangle with the span of the Soil as the hypotenuse and the vertical separate from the center of the Soil to the beat of the hot discuss swell as the inverse side. The radius of the Soil is around 4000 miles, and the stature of the swell is 1.2 miles.
Utilizing trigonometry, able to calculate the point θ (in radians) utilizing the equation:
θ = arcsin(opposite / hypotenuse)
θ = arcsin(1.2 / 4000)
θ ≈ 0.000286478 radians
To discover the degree of the circular segment in degrees, we will change over the point from radians to degrees:
Arc measure (in degrees) = θ * (180 / π)
Arc measure ≈ 0.000286478 * (180 / π)
Arc measure ≈ 0.0164 degrees
Adjusted to the closest tenth, the arc degree representing the portion of Soil you'll see from the hot air balloon is around 0.0 degrees.
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Joey needs to buy chocolate milk they only sell it in pint containers how many pint containers of chocolate milk should he buy
To determin how many pint containers of chocolate milk Joey should buy, we need to know how much chocolate milk he wants in total.
Let's assume Joey wants to buy "x" pints of chocolate milk. Then, the total amount of chocolate milk he will get in quarts can be calculated as:
Total amount of chocolate milk = x pints/2 pints per quart = x/2 quarts
If Joey has a specific total amount of chocolate milk he wants to buy, we can solve for "x". For example, if Joey wants to buy 3 quarts of chocolate milk, we can set up the following equation:
x/2 = 3
Multiplying both sides by 2, we get:
x = 6
So, Joey needs to buy 6 pint containers of chocolate milk to get 3 quarts in total.
If Joey has a different desired amount of chocolate milk, we can adjust the equation accordingly to find the number of pint containers he needs to buy
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Please help guys please
Answer: The answer is A
Step-by-step explanation:
Which of the following would solve the equation below for x in onestep?10=x-15A. Adding 15 to both sides of the equationB. Adding 10 to both sides of the equationC. Subtracting 15 to both sides of the equationD. Subtracting 10 to both sides of the equation
In order to solve the equation for x, we need to look at the side where the variable is, then, we apply the contrary operations to this operation on both sides.
In this case, x is being subtracted by 15, then we need to eliminate this 15 by adding 15 on both sides
\(\begin{gathered} 10+15=x-15+15 \\ 25=x \end{gathered}\)Answer:
A. Adding 15 to both sides of the equation
Nora drives 100 miles in 2 hours. what is her rate per hour?
If g(x)= 2x +8x-1 what is g(-3)
A) -7
B) 11
C) 28
D)7
Step-by-step explanation:
Greetings !
Firstly, write down the given expression
\(g(x) = 2x + 8x - 1\)
simplify it to be more accurate where 2+8=10
\(g(x) = 10x - 1\)
plug in -3 in the value of x and simplify the expression
\(g( -3 ) = 10( - 3) - 1 \\ g( - 3) = - 30 - 1\)
Thus, subtract the numbers
\(g( - 3) = - 31\)
Hope it helps!
What is the linear function equation that best fits the data set? 1) y = -2x + 5. 2) y = 2x + 5. 3) y = -1/2x + 5. 4) y = 1/2x - 5.
Without specific information about the data set, it is not possible to determine which equation is the best fit.
To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.
However, I can provide a general explanation of the four options:
y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.
y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.
y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.
y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.
Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.
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what is th answer to this question
The total surface area of the trapezoidal prism is S = 3,296 inches²
Given data ,
Let the total surface area of the trapezoidal prism is S
Now , the measures of the sides of the prism are
Side a = 10 inches
Side b = 32 inches
Side c = 10 inches
Side d = 20 inches
Length l = 40 inches
Height h = 8 inches
Lateral area of prism L = l ( a + b + c + d )
L = 40 ( 10 + 32 + 10 + 20 )
L = 2,880 inches²
Surface area S = h ( b + d ) + L
On simplifying the equation , we get
S = 2,880 inches² + 8 ( 52 )
S = 3,296 inches²
Hence , the surface area of prism is S = 3,296 inches²
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find the general solution of the differential equation ′()=(5−3) 8. (use symbolic notation and fractions where needed. give your answer in the form ⟨(),(),()⟩. )
The answer is ⟨y(x) = (-1/27)(5 - 3x)^9 + C, where C is an arbitrary constant⟩.
How to find the general solution of the differential equation ′()=(5−3) 8?The given differential equation is:
y' = (5 - 3x)^8
We can separate the variables and integrate both sides:
dy/dx = (5 - 3x)^8
dy = (5 - 3x)^8 dx
Integrating both sides, we get:
∫dy = ∫(5 - 3x)^8 dx
y = (-1/27)(5 - 3x)^9 + C
where C is an arbitrary constant of integration.
Therefore, the general solution of the differential equation is:
y(x) = (-1/27)(5 - 3x)^9 + C
where C is an arbitrary constant.
Hence, the answer is ⟨y(x) = (-1/27)(5 - 3x)^9 + C, where C is an arbitrary constant⟩.
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12 + 36 /3 × 4 + 300
When talking about a scale drawing or model, _____________ is determined by the ratio of a given length on the drawing or model to its corresponding length on the actual object. How do we write this as a fraction?
When talking about a scale drawing or model, the scale factor is determined by the ratio of a given length on the drawing or model to its corresponding length on the actual object.
This can be written as a fraction, with the length on the drawing or model as the numerator and the corresponding length on the actual object as the denominator. For example, if a drawing of a building has a scale factor of 1:100 and the length of a wall on the drawing is 5 cm, the corresponding length on the actual building would be 500 cm (5 cm x 100). Therefore, the scale factor can be written as 5/500 or simplified to 1/100.
When talking about a scale drawing or model, the term you're looking for is "scale factor." It is determined by the ratio of a given length on the drawing or model to its corresponding length on the actual object. To write this as a fraction, you would place the length on the drawing or model as the numerator and the corresponding length on the actual object as the denominator. For example, if the scale factor is 1:10, you would write it as 1/10.
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what the simplified form of 3
Answer:
It’s the last one.
Step-by-step explanation:
135 can also be written as 9 times 15. Since this is a square root, find a factor that is repeated twice. 9 can be broken down into 3 times 3. Hence this goes on the outside. 15 stays inside.
identify the transformation
Either as a translation, reflection, or rotation.
PLEASE HELP ME
Answer: Rotation
Step-by-step explanation:
If we look at the shapes, we can see that TSVU is rotated around point U into shape YWXU.
Reflection means the point is directly reflected, like a mirror.
Translation means the shape is moved in a direction (like up or down).
Rotation means the shape is spun around, like a clock. Here, the shape is rotated.