Answer:
0.075 is a hundred times smaller than 7.5
Step-by-step explanation:
The nutrition information on the cereal box says that a 1/2-cup serving provides 210 calories and 9 grams of dietary fiber. At that rate, find how many calories and grams of fiber are in a 2/3-cup serving.
Answer:
280 calories and 12 grams of dietary fiber
Step-by-step explanation:
because 210(2/3) = 140
= 140 ÷ 1/2 = 280
we do the same steps with grams
9(2/3) = 6
= 6 ÷ 1/2 = 12
Find an equation for the perpendicular bisector of the line segment whose endpoints are (−2 ,− 9) and (−6,7). PLSLLSLS
The equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The midpoint of the line segment joining (-2, -9) and (-6, 7) can be found using the midpoint formula:
Midpoint = ( (x₁+x₁)/2 , (y₁+y₁)/2 )
Midpoint = ( (-2-6)/2 , (-9+7)/2 )
Midpoint = (-4,-1)
Next, we need to find the slope of the line joining the two points (-2, -9) and (-6, 7). We can do this using the slope formula:
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (7 - (-9)) / (-6 - (-2))
Slope = 4
The slope of the line perpendicular to the line segment is the negative reciprocal of the slope of the line joining the two points. So the slope of the perpendicular line is -1/4.
Using the point-slope form of a line, the equation of the perpendicular bisector can be written as:
y - y₁ = m(x - x₁), where (x₁, y₁) is the midpoint and m is the slope of the line.
Plugging in the values we found, we get:
y - (-1) = (-1/4)(x - (-4))
y + 1 = (-1/4)(x + 4)
y + 1 = (-1/4)x - 1
y = (-1/4)x - 2
Therefore, the equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2.
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h(n) =4n+2
g(n)= n³ +5 - 2n
Find 3h(n) + 2g(n)
The solution of the expression 3h(n) + 2g(n) will be 2n³ -8n +16.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that the two values are h(n) =4n+2 and g(n)= n³ +5 - 2n. The value of the expression 3h(n) + 2g(n) will be calculated as:-
E = 3h(n) + 2g(n)
E = 3 ( 4n+2 ) + 2 (n³ +5 - 2n)
E = 12n + 6 + 2n³ + 10 -4n
E = 2n³ + 8n + 6
Therefore, the answer to the equation 3h(n) + 2g(n) is 2n3 -8n +16.
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PLEASE HELP WILL GIVE BRAINIEST!!
At what point does the graph of a function of this form start?
The start point the graph of a function of this form is (h, k)
How to determine the start of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = a√(x - h) + k
The domain is given as
x ≥ h
This means that the initial x value is h
From the question, we have the following parameters that can be used in our computation:
f(h) = a√(h - h) + k
Evaluate
f(h) = k
Hence, teh initial point is (h, k)
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Use the formula V = Bh to calculate the volume of a cylinder that has a diameter of 6 centimeters and a height of 8 centimeters. Express your answer in terms of pi.
The volume of the cylinder is 72π cubic centimeters.
What is volume?
Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.
For solid objects, volume refers to the amount of space the object occupies in three-dimensional space.
The formula for the volume of a cylinder is:
V = Bh
where B is the area of the base of the cylinder, and h is the height of the cylinder.
In this problem, the cylinder has a diameter of 6 centimeters, which means the radius is 3 centimeters. The area of the base of the cylinder is therefore:
B = πr²
B = π(3 cm)²
B = 9π cm²
The height of the cylinder is given as 8 centimeters. Therefore, we can use the formula for the volume of a cylinder to find the volume V:
V = Bh
V = (9π cm²)(8 cm)
V = 72π cubic centimeters
Therefore, The volume of the cylinder is 72π cubic centimeters.
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Graph the line with slope 2 passing through the point (-3, -4).
The solution is, the equation is y=2/3x.
What is meant by graph?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
A diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.
here, we have,
so the line is in slope intercept form
y=mx+b, m=slope and b=y intercept
we know the slope so just solve for b
y=2/3x+b
subsitute
3 for x and 2 for y
2=2/3(3)+b
2=2+b
subtract 2 from both sdies
0=b
so the equaiton is
y=2/3x+0 or just simply
y=2/3x
here is the graph
just input values for x and get y values exg
x=3 y=2
x=6 y=4
x=0 y=0
x=-3 y=-2
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Write the inequality shown by the shaded region in the graph with the boundary line −5x+2y=−2
Answer:
Step-by-step explanation:
The boundary line of the shaded region in the graph, which is represented by the equation -5x + 2y = -2, can be used to write the inequality that represents the shaded region. To do this, we first need to determine which side of the boundary line the shaded region is on.
If the shaded region is on the same side of the line as the open half-plane that contains the y-axis, then the inequality is given by:
-5x + 2y > -2
If the shaded region is on the same side of the line as the closed half-plane that does not contain the y-axis, then the inequality is given by:
-5x + 2y ≥ -2
So, the inequality that represents the shaded region depends on the specific context and requirements of the problem, as well as the interpretation of the graph.
Sears is having a 35% off sale on all tires. Michelin tires sells for $125, find the Sales Price.
Answer:
You will pay 81.25
Step-by-step explanation:
If the cost is 35% off, you will need to pay 100% - 35% = 65%
125 * 65 %
125 *.65
81.25
You will pay 81.25
What is a common factor for the two fractional terms
5
8
The terms can be written as (5)
05
-100 100
y
(x) and (11)
11
8
x and.
(x) (y).
xy?
Answer:
Step-by-step explanation: Yes, that is correct. The solution to the system of equations is (x, y) = (-7, 0), which is not in the given options, so none of the options are the correct answer.
Which of the following equations listed below are linear equations?
Only Equation I is a linear equation. A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line.
What is Straight line?
A straight line is a type of geometric shape that is defined as a line with no curvature, extending infinitely in both directions. In other words, it is a one-dimensional object that extends indefinitely without bending or curving. Straight lines are often represented mathematically as y = mx + b, where m is the slope (or gradient) of the line and b is the y-intercept.The slope determines the steepness of the line, and the y-intercept determines where the line crosses the y-axis. Straight lines play a crucial role in mathematics, especially in geometry and linear algebra.
Only Equation I is a linear equation.
A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line. In Equation I, P is equal to 4 times s, so the highest power of the variable (s) is 1, making this a linear equation.
In Equation II, the right-hand side of the equation contains a single constant ($3), not a variable, and therefore it is not a linear equation.
Equation III is not a linear equation because it is just a constant equal to 2 and does not contain a variable.
So the answer is: 1. Equation I, only.
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A set of data has a mean of 10 and a standard deviation of 3.
(a) Each value in the data set has 6 added to it. Write down the value of
(i) the new mean;
(ii) the new standard deviation.
(b) Each value in the original data set is multiplied by 6.
(i) Write down the value of the new mean.
(ii) Find the value of the new variance.
Answer:
Step-by-step explanation:
(a) (i) The mean of the original data set is denoted as μ and the constant value being added to each data point is denoted as c.
The formula for the new mean is simply μ + c, so the new mean is μ + 6 = 10 + 6 = 16.
(a) (ii) The standard deviation of the original data set is denoted as σ. Adding a constant value to each data point does not change the spread of the data set, so the new standard deviation is still σ = 3.
(b) (i) The mean of the original data set is denoted as μ and the constant value being multiplied to each data point is denoted as k.
The formula for the new mean is μ * k, so the new mean is μ * 6 = 10 * 6 = 60.
(b) (ii) The variance of the original data set is denoted as V. To find the new variance after multiplying each data point by k, we can use the formula: k^2 * V.
So, the new variance is 6^2 * V = 36 * V.
--------
Here is a definition of each variable:
μ: The mean of a set of data is the sum of all the values divided by the number of values. It represents the average value of the data set.
σ: The standard deviation of a set of data is a measure of the spread of the data set about the mean. It is the square root of the variance.
V: The variance of a set of data is the sum of the squares of the deviations of each value from the mean, divided by the number of values. It is a measure of the spread of the data set about the mean, but it is measured in squared units.
c: A constant value added to each data point.
k: A constant value multiplied to each data point.
Select the correct answer. In which of the scenarios can you reverse the dependent and independent variables while keeping the interpretation of the slope meaningful? A. As the number of cigarettes smoked in a day increases, the risk for lung cancer increases. B. As the age of an infant increases, the height of the infant increases. C. As the number of vehicles in a city increases, the amount of pollution in the city increases. D. As the concentration of salt in water increases, the density of water increases. E. As the number of calls made by a cell phone increases, the cell phone bill amount increases.
The scenarios can you reverse the dependent and independent variables while keeping the interpretation of the slope meaningful in
E) As the number of calls made by a cell phone increases, the cell phone bill amount increases.
What is Independent and Dependent Variable?We anticipate that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.
Given:
We can see from Option A that the opposite may not be true, as an increase in the risk of lung cancer may not always be accompanied by an increase in the number of cigarettes smoked each day.
Now, second it is clear that the opposite may not be true because an infant's age may not necessarily increase along with his or her height.
Now, third also acknowledges that a rise in traffic is not always accompanied by an increase in pollution in a city.
Fourth, a rise in water density does not always imply an increase in the amount of salt present in the water.
Only in Option E do we find a potential reverse reliance because a rise in phone bill amount does typically correspond to a rise in cell phone call volume.
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You randomly survey middle school students and high school students about whether they prefer spring or winter. The results
are shown in the two-way table. Find the percent of middle school students that prefer each season and the percent of high school students that prefer each season
The percentage of middle school students that prefer each season and the percentage of high school students that prefer each season is 57.93% and 42.07% respectively.
What is the percentage?The percentage is the ratio of the composition of value to the overall composition of value multiplied by 100.
Here,
Total number of students = 93 + 31 + 36 + 54 = 214
The percentage of students in middle school prefer spring,
= number of students in middle school prefer spring / total student × 100%
= 93/214 × 100%
= 43.45%
Similarly,
The percentage of students in middle school prefer winter,
= number of students in middle school who prefer winter/ total students × 100%
= 31/214 × 100%
= 14.48%
Thus, the percentage of middle school students that prefer each season and the percentage of high school students that prefer each season are 43.45 + 14.48 = 57.93% and 100-57.93% = 42.07%.
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Yasmin is participating in a 5-day cross-country biking challenge. She biked for 45,60,68 and 52 kilometers on the first four days. How many kilometers does she need to bike on the last day so that her average (mean) is 58 kilometers per day?
Step-by-step explanation:
The total distance biked by Yasmin on the first four days can be calculated as follows:
45 + 60 + 68 + 52 = 225 km
To find out how many kilometers she needs to bike on the last day to achieve an average of 58 km per day over the 5 days, we can set up an equation based on the formula for the mean:
(45 + 60 + 68 + 52 + x) / 5 = 58
Where x is the number of kilometers Yasmin needs to bike on the last day. Expanding the equation:
225 + x = 5 * 58
225 + x = 290
Subtracting 225 from both sides:
x = 65
So Yasmin needs to bike 65 kilometers on the last day to achieve an average of 58 kilometers per day over the 5 days
Greta’s family drinks 3. 1/4 quarts of milk and 1 5/6 quarts of juice in one week. About how much more milk than juice does Greta’s family drink in one week?
Answer:1 5/12 or written the other way 17/12
Step-by-step explanation:
petra jogs 60 miles in 110 minutes, at this rate how long would her take to jog per one minutes
The speed of Petra will be 0.55 mile/minute.
What exactly is speed?
The definition of speed is:
The pace at which an object's location changes in any direction.
Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no magnitude, speed is a scalar number.
Formula for Speed
The speed formula is shown below:
s=d/t
Where,
s is the speed in metres per second, d is the distance travelled in metres, and t is the duration in seconds.
Now,
As given petra jogs 60 miles in 110 minutes
then in one minute she will jog =60/110 mile
=0.5454 mile/min
Hence,
The speed of Petra will be 0.55 mile/minute.
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You borrow $900 and agree to repay it with 11% interest.
How much interest will you owe?
The interest to be paid is $99
What is simple interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Simple Interest = P×R×T/100
where P is the principal,
R is the rate
and T is the time
P = $900
R = 11%
T= 1
I = 900× 11/100
I = $99
therefore the interest to be paid is $99
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Which expression is equivalent to
The expression equivalent to 5x +10y -15 by taking the common factor is 5(x + 2y - 3).
What is taking out common factors?
The takeout of the common factor is the procedure, ab + ac = a(b + c). Think about how the expression 5x + 10 gets factored. The common factor 5, which was previously in front of the brackets, has been removed.
Figuring out what to multiply to create an expression. It is comparable to "splitting" an expression into numerous smaller expressions.
Given, the expression is 5x + 10y -15
So, 5x +10y -15 = 5x + 5*2y - 5*3
= 5(x + 2y - 3)
Hence, the required answer is 5(x + 2y - 3).
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I can’t find this answer please help me.
Reason: Split the angle 155 in half to get 155/2 = 77.5
A company made 500 flashlights and found that 5 were defective. If the company makes 12,500 flashligh
O 120
O125
0 250
O 1,250
The company can expect to find 125 defective flashlights in a production run of 12,500. The correct option is B, 125.
What is flashlights?Flashlight can be defined as a portable, battery-operated device used for illumination. It typical unit consists of one or more dry cell batteries arranged in a line inside a battery compartment that forms the handle of the light.
Assuming the proportion of defective flashlights remains the same, the number of defective flashlights in a production run of 12,500 would be:
(5/500) x 12,500 = 125
Therefore, the company can expect to find 125 defective flashlights in a production run of 12,500. The answer is option B, 125.
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A. 30.28 square feet
B. 24.28 square feet
C. 36.56 square feet
D. 30.56 square feet
Answer:
B. 24.28 square feet
Step-by-step explanation:
You want the area of a figure composed of a rectangle, triangle, and semicircle.
Area formulasThe formulas for the areas of the parts of the figure are ...
A = LW . . . . rectangle of length L and width W
A = 1/2bh . . . . triangle with base b and height h
A = π/2r² . . . . . . semicircle of radius r
RectangleThe area of the rectangle is ...
A = (4 ft)(3 ft) = 12 ft²
TriangleThe area of the triangle is ...
A = 1/2(4 ft)(3 ft) = 6 ft²
SemicircleThe semicircle has a radius that is half the diameter. The diameter is shown as 4 ft so the radius is 2 ft. The area of the semicircle is ...
A = π/2(2 ft)² = 4(3.14)/2 ft² = 6.28 ft²
Composite figure areaThe area of the composite figure is the sum of the areas of its parts:
Area = 12 ft² +6 ft² +6.28 ft² = 24.28 ft²
The area of the composite figure is about 24.28 ft².
Faith invests £800 for 3 years in a bank account. The account pays simple interest at a rate of 0.4% per year Work out the total amount of interest Faith has got at the end of the 3 years.
?
equation or inequality best
75x + 0.55y = 125
The solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 75x + 0.55y = 125.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Substitute x=0, 1, 2, 3, 4, 5,....
When x=0
75(0)+0.55y=125
0.55y=125
y=125/0.55
y=227
When x=1
75(1)+0.55y=125
0.55y=50
y=50/0.55
y=91
When x=2
75(2)+0.55y=125
0.55y=-25
y=-25/0.55
y=-45.45
Therefore, the solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)
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please hel me.
i need help i don't know how to do this
The tables with their equations are
Table (a): y = 1/xTable (b): y = √xTable (c): y = x³Table (d): y = xHow to match the tables with their equationsFrom the question, we have the following parameters that can be used in our computation:
Tables and equations
Table (a)
Here, we notice that:
The output is the reciprocal of the input
This is represented as
y = 1/x
Table (b)
Here, we notice that:
The output is the square root of the input
This is represented as
y = √x
Table (c)
Here, we notice that:
The output is the cube of the input
This is represented as
y = x³
Table (d)
Here, we notice that:
The output is the same as the input
This is represented as
y = x
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Mrs. Smith baked 2 cakes. There are seven people in her family. How much of the cakes can each person have? Make sure to write your answer as a simplified fraction.
The required, each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.
What is the fraction?A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.
here,
To divide the 2 cakes equally among 7 people, we can use division. We can think of the total amount of cake as 2 whole cakes or 2/1 cakes. To find out how much cake each person can have, we can divide the total amount of cake by the number of people:
2/1 cakes ÷ 7 people = 2/1 × 1/7 = 2/7 cakes per person
So each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.
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Car 1 is traveling a 7 m/s and has a mass 3000kg. Car 2 is stopped and has a mass of 8000 kg. If the two cars collide and couple , what will be their final velocity?
If the two cars collide and couple, then their final velocity will be 1.91 meters per second.
What is conservation of momentum?According to the principle of momentum conservation, movements are only modified by the action of forces as they are outlined by Newton's equations of motion; momentum is never generated nor destroyed inside a problem domain.
The conservation of momentum is given as,
m₁u₁ + m₂u₂ = (m₁ + 2₂)v
Car 1 is moving at a speed of 7 m/s and weighs 3000 kg. Car 2 is not moving and weighs 8000 kg.
3,000 x 7 + 8,000 x (0) = (3,000 + 8,000) x v
21,000 + 0 = 11,000v
v = 21,000 / 11,000
v = 1.91 meters per second
If the two cars collide and couple, then their final velocity will be 1.91 meters per second.
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Solve for A.
W=A/6.
Help please.
Thank you! TIA
Answer:
A = w*6
Step-by-step explanation:
W = A/6
Multiply both sides by 6 using the multiplication property of equality.
A = W*6
or
A = W x 6
Hope this helps!
Fill in the sentence below with the description that most specifically
applies to the quadrilateral below.
X
117
The quadrilateral is most specifically a
because
The quadrilateral is most specifically a square since all the sides of the quadrilateral are equal and have 90°
What is the area of a square?A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.
A square is a 4 sided polygon where all the sides are of equal length.
The area of the square is the square of any one of its side
Let a be the side of the square
Area of the square = a²
Given data ,
Let the quadrilateral be represented as ABCD
Now , the measures of the sides of the quadrilateral are
The measure of side AB = measure of side BC
And , the measure of side AB = measure of side AD
So , all the 4 sides of the quadrilateral are same so it is a square
And the measures of angles are 90° each
Therefore , the quadrilateral is a square
Hence , it is a square
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What is the answer? Provide steps please.
The given expression is proved.
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
here, we have.
tan∅/(1+ sec∅)
=(sin∅/cos∅)/(1+ sec∅) [tan∅=(sin∅/cos∅)]
=(sin∅/cos∅)/(1+1/cos∅)
=sin∅/1+cos∅
multiplying both numerator & denominator by 1-cos∅, we get,
=sin∅(1-cos∅)/ sin^2∅
=(1-cos∅)/sin∅
=cosec∅ - cot∅
Hence, The given expression is proved.
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Solve for x, each figure is a trapezoid
By calculating , The value of x we get is 5 as a final resultant.
What is trapezoid ?
A trapezoid is a quadrilateral with two parallel sides, called the "bases," and two non-parallel sides, called the "legs." The parallel sides can have different lengths, and the trapezoid can be either right-angled or oblique. In other words, a trapezoid is a geometric shape that has two parallel sides, two non-parallel sides and four angles.
Since a Trapezoid has 360 Degrees total and since the sides are equal we can say that
180=110+17x-15
70=17x-15
85=17x
x=5
Therefore, By calculating , The value of x we get is 5 as a final resultant.
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