a + 8. This expression represents the total number of almonds that Daniel snacked on in all.
What is the difference between expression and equation?
An expression is a mathematical phrase that contains numbers, variables, and operations. It can be evaluated to produce a single numerical value or another expression. Expressions do not contain an equal sign (=), and they do not represent a statement that is either true or false.
An equation, on the other hand, is a mathematical statement that shows the equality between two expressions. It contains an equal sign (=) and represents a statement that is either true or false. Equations typically contain variables that can take on different values, and they can be used to solve for an unknown variable by manipulating the equation using algebraic operations.
To summarize, expressions are mathematical phrases that do not contain an equal sign and can be evaluated to produce a value, while equations are mathematical statements that do contain an equal sign and represent a relationship between two expressions that is either true or false.
We can use addition to represent the total number of almonds that Daniel snacked on. If Daniel snacked on an initial amount of almonds, say "a", and then snacked on an additional 8 almonds, we can write the expression:
a + 8
This expression represents the total number of almonds that Daniel snacked on in all.
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Find an equation for the line that passes through the points (- 1, -6) and (3, 4)
Answer:
y=5/2x-7/2
Step-by-step explanation:
A jar contains three blue marbles ,seven red marbles and five green marbles,and you pick one without looking.What is the probability that the marble will be neither red nor blue
Answer:1 in 3 chance
Step-by-step explanation:
There are 5 green, 3 blue, and 7 red. Add them up 5+3+7=15
Then you put it into a fraction [tex]\frac{5}{15} =\frac{1}{3} \\[/tex]
1 over 3 is your answer
Given the linear function f(x) = −4x + 8, what is the value of x if f(x) = 24?
x = 104
x = −4
x = −8
x = −88
Answer:
The value of x = -4
Step-by-step explanation:
The given linear function is f(x) = -4x+8
We have to find the x corresponding to f(x) = 24
For our convenience, let f(x) = y
Then y = -4x + 8
This equation implies y in terms of x.
Isolating x to one side of the equation, we get,
x = (y - 8)/-4 = (8-y)/4
This equation gives x in terms of y.
So when f(x) = y = 24,
x = (8-24)/4
⇒ x = -4
What are all possible values of x that satisfy the inequality x3−8≥1?
We have the following response after answering the given question: inequality {x | x ≥ ∛9} or [∛9, ∞) in interval notation.
What is inequality?A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.
[tex]x^3[/tex] - 8 ≥ 1
Adding 8 to both sides, we get:
[tex]x^3[/tex] ≥ 9
Taking the cube root of both sides, we get:
x ≥ ∛9
Since ∛9 is approximately 2.08, the inequality is satisfied for all values of x greater than or equal to 2.08. Therefore, the set of all possible values of x that satisfy the inequality is:
{x | x ≥ ∛9} or [∛9, ∞) in interval notation.
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Find sin 8.
45
53
28
8
Answer:
A. 45/53
Step-by-step explanation:
.............
Answer:
A. 45/53
Step-by-step explanation:
sin ø is A.
have a nice day
3(x+7) in distributive property then in expanded form
Answer:
Using the distributive property on 3(x+7), we get:
3(x+7) = 3x + 37
Simplifying the expression, we get:
3(x+7) = 3x + 21
Therefore, in expanded form, 3(x+7) is equal to 3x + 21.
3.Jason needs at least 260 eggs for a charity breakfast. He writes the inequality
12d+72 ≥ 260 to represent the number of dozens of eggs, d, that he needs to buy
since he already has 72 eggs. Which statement best explains whether d = 7 is a solution to
Jason's inequality?
A. d= 7 is a solution because 12 x 7 = 84 and 84 is greater than 72.
B. d= 7 is a solution because 12 x 7 + 72 = 156 and 156 is less than 260.
C. d= 7 is not a solution because 127 + 72 = 199 and 199 is less than 260.
D. d= 7 is not a solution because 12 x 7+72 = 156 and 156 is less than 260.
Answer:
The answer is D hope this helps:)
Step-by-step explanation:
Question 5
Kayleigh and Allison race. Kayleigh runs 5 miles per hour. Allison runs 3 miles per hour but has a 1 mile head
start. Using the formulas below where h is hours and d is distance, how long does it take before they meet
each other in the race?
Kayleigh d = 5h
Allison d = 3h+1
Answer:
Let's call the time it takes for Kayleigh and Allison to meet each other "t".
We know that Kayleigh runs at a constant rate of 5 miles per hour, so the distance she covers in "t" hours is given by:
Kayleigh's distance = Kayleigh's speed * time = 5t
Allison runs at a constant rate of 3 miles per hour, but she has a 1 mile head start. This means that by the time Kayleigh and Allison meet each other, Allison will have run "t" hours minus the time it took her to cover her head start distance. The time it takes Allison to cover her head start distance is:
Time for Allison's head start = distance / speed = 1 / 3 = 0.33 hours (rounded to two decimal places)
Therefore, when Kayleigh and Allison meet each other, Allison will have run:
Allison's distance = Allison's speed * (t - 0.33) = 3(t - 0.33)
Now, we know that when they meet, Kayleigh's distance is equal to Allison's distance:
Kayleigh's distance = Allison's distance
5t = 3(t - 0.33)
Simplifying and solving for "t", we get:
5t = 3t - 1
2t = 1
t = 0.5
Therefore, it takes Kayleigh and Allison 0.5 hours (or 30 minutes) to meet each other in the race.
In the circle below, suppose m WXU = 152° and mXWV=71°. Find the following.
(a) mWXU =
(b) mXUV =
The value of angle mXUV is 76⁰.
The value of angle mXUV is 109⁰.
What is the value of angle mWXU ?
The measure of angle mWXU is calculated by applying the following circle theorem.
mWXU = ¹/₂ ( 152⁰ ) (angle at tangent is half the angle subtended by an arc )
mWXU = 76⁰
The value of angle mXUV is calculated as follows;
mXUV + mXWV = 180 (opposite angles of a cyclic quadrilateral)
mXWV + 71 = 180
mXWV = 180 - 71
mXWV = 109⁰
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Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that 12 people will be randomly chosen to be on the committee from a group of 30 volunteers, 21 who are technically proficient and 9 who are not. We are interested in the number on the committee who are not technically proficient.
c)How many instructors do you expect on the committee who are not technically proficient? (Round your answer to the nearest whole number.)
(d)Find the probability that at least 3 on the committee are not technically proficient. (Round your answer to four decimal places.)
(e)Find the probability that at most 4 on the committee are not technically proficient. (Round your answer to four decimal places.)
The prοbability that nο mοre than fοur cοmmittee members are technοlοgically adept is 0.9851, rοunded tο fοur decimal places.
c) By dividing the tοtal number οf applicants whο are nοt technically prοficient (9) by the likelihοοd that any οne οf them wοuld be selected fοr the cοmmittee, it is pοssible tο calculate the anticipated number οf instructοrs οn the cοmmittee whο are nοt technically prοficient:
Number anticipated: 9 * (12/30) = 3.6
Tο the nearest whοle number, we estimate that there will be fοur prοfessοrs οn the cοmmittee whο lack technical prοficiency.
d) We can use the binοmial distributiοn with n=12 (the number οf trials) and p=0.3 tο determine the likelihοοd that at least three members οf the cοmmittee lack technical prοficiency (prοbability οf success, which is defined as selecting a vοlunteer whο is nοt technically prοficient). When X is the number οf technically incοmpetent prοfessοrs οn the cοmmittee, we want tο determine P(X>=3).
P(X>=3) = 1 - P(X<3)
= 1 - P(X=0) - P(X=1) - P(X=2)
[tex]\mathrm{=1 - (12\ choose\ 0)(0.3^0)(0.7^{12}) - (12\ choose\ 1)(0.3^{1})(0.7^{11}) - (12\ choose\ 2)(0.3^2)(0.7^{10)}}[/tex]
[tex]= 1 - 0.00744 - 0.0563 - 0.1667[/tex]
[tex]= 0.7696[/tex]
The likelihοοd that at least three members οf the cοmmittee lack technical prοficiency is 0.7696, rοunded tο fοur decimal places.
e) Using the same binοmial distributiοn as in part d), we can calculate the likelihοοd that at mοst 4 members οf the cοmmittee are nοt technically adept by adding the prοbabilities fοr X=0, 1, 2, 3, and 4:
P(X<=4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)
[tex]\mathrm{= (12\ choose\ 0)(0.3^0)(0.7^{12}) + (12 \ choose\1)(0.3^1)(0.7^|{11}) + (12 \ choose\2)(0.3^2)(0.7^{10})}\\\mathrm{ + (12 \ choose\3)(0.3^3)(0.7^9) + (12 \ choose\4)(0.3^4)(0.7^8)}[/tex]
[tex]= 0.9851[/tex]
Rounding tο four decimal places, the likelihood that no more than four committee members are technοlogically savvy is 0.9851.
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Andrea and her friend were planning to paint Andrea’s aunt's fence this summer.The last time Andrea painted the fence alone the painting job took her 6 hours. Her friend had painted a similar fence or similar surface area in 4 hours. Which is the best estimate of the time it will take Andrew and her friend to paint the fence together?
The best estimate of the time it will take Andrea and her friend to paint the fence together is 2.4 hours.
What is work and time in mathematics?
In mathematics, work refers to the amount of effort or energy needed to complete a task or achieve a goal. Work is often measured in units such as joules or calories.
Time refers to the duration or amount of time it takes to complete a task or achieve a goal. Time is often measured in units such as seconds, minutes, hours, or days.
To estimate the time it will take Andrea and her friend to paint the fence together, we can use the formula:
Total Time = (Time for Person 1 x Time for Person 2) / (Time for Person 1 + Time for Person 2)
Using this formula, we can estimate the time it will take Andrea and her friend to paint the fence together as:
Total Time = (6 hours x 4 hours) / (6 hours + 4 hours) = 24/10 = 2.4 hours
Therefore, the best estimate of the time it will take Andrea and her friend to paint the fence together is 2.4 hours.
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Sadie is planning to go paddleboarding this weekend, but wants to know the water temperature at the lake so she can wear the correct gear. The lake temperature is reported to be 10.5 °C today. After a few sunny days, it should be 1.5 °C warmer this weekend.
what will the water temperature be this weekend in F°?
Answer:
To convert from Celsius to Fahrenheit, we can use the formula F = (C × 1.8) + 32.
First, we need to convert 10.5 °C to Fahrenheit:
F = (10.5 × 1.8) + 32
F = 18.9 + 32
F = 50.9 °F
Then, we can add the 1.5 °C increase in temperature:
New C temperature = 10.5 + 1.5 = 12 °C
And convert that to Fahrenheit using the same formula:
F = (12 × 1.8) + 32
F = 21.6 + 32
F = 54.6 °F
Therefore, the water temperature this weekend in F° will be approximately 54.6 °F.
The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder? Question 8 options: 350 m3 700 m3 437.5 m3 175 m3 70 m3
With a scaling ratio of 5:2, the larger cylinder's volume is (C) 70m³.
What is the scale factor?A scale factor is used when a shape is enlarged and each side is multiplied by the same quantity.
This number represents the scaling factor. Map scale factors are used to show distances between locations accurately.
The new shape created by scaling the original shape is twice as big when the scale factor is 2.
Thus, calculate the larger cylinder's volume as follows:
x/5 = 28/2
2x = 28*5
2x = 140
x = 70m³
Therefore, with a scaling ratio of 5:2, the larger cylinder's volume is (C) 70m³.
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Complete question:
The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder?
Question 8 options:
A. 700 m3
B. 350 m3
C. 70 m3
D, 437.5 m3
E. 175 m3
Answer: 70m^3
Step-by-step explanation:
I took the test
12. A mosaic wall is divided into 100 equal
Name
sections. If 30 sections are reserved for
orange tiles and 40 sections are reserved
for blue tiles, what fraction of the mosaic
wall is left for other colors?
Answer:
There are 30 + 40 = 70 sections reserved for orange and blue tiles. This means there are 100 - 70 = 30 sections left for other colors.
To express the fraction of the mosaic wall left for other colors, we can write:
30 sections left / 100 total sections = 3/10
Therefore, the fraction of the mosaic wall left for other colors is 3/10.
A swimming pool is draining at a constant rate. The amount of water in gallons left in the pool after X minutes is represented by the expression shown.
25,000-30x
What does 30 represent in this context?
So, 30 reflects the amount of water that is being removed from the swimming pool per minute in gallons.
How variables figure out an equation?In the provided formula, 25,000 - 30x, x is the amount of time in minutes and 30 is the pace in gallons per minute at which the pool is draining.
The expression is a linear equation of the form y = mx + b, where x is the length of time that has passed and y is the amount of water that is still in the pool.
The slope (m) of the equation in this instance is -30, which means that the pool's water level is dropping at a rate of 30 gallons per minute.
The expression's value decreases as more time passes because the value of x rises. As a result of the water draining out of the pool at a constant rate of 30 gallons per minute, the pool's volume is dropping linearly over time.
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For a binomial probability distribution, let n = 6 and p = 0.2608. Determine the probability of five successes. (Use 4 decimal places.)
The probability of five successes where the number of trials is 6 and the probability of success is p = 0.2608, for the binomial probability distribution is; P(x = 5) = 0.00535
What is the binomial probability function?The binomial probability function can be expressed as follows;
Pₓ = [tex]\binom{n}{k}[/tex] × Pˣ × (1 - P)⁽ⁿ ⁻ ˣ⁾
Where;
P = The probability of success
x = The number of successes
n = The number of trials
The details from the question includes;
The type of probability distribution = Binomial probability distribution
The number of trials = 6
The probability of success = 0.2608
Therefore;
The probability of success, P = 0.2608
Number of trials, n = 6
The required number of successes, x = 5
Plugging in the above values in the binomial probability formula , we get;
P₅ = [tex]\binom{6}{5}[/tex] × 0.2608⁵ × (1 - 0.2608)⁽⁶ ⁻ ⁵⁾ = 6 × 0.2608⁵ × (1 - 0.2608)⁽⁶ ⁻ ⁵⁾ ≈ 0.0054
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Divide Katrina's number line into
eighths. Divide Eric's number line into
fourths. Show a point on Katrina's
number line that is less than 1. Show
a point on Eric's number line that is
greater than 1. Write fractions to label
the points you picked.
1. A point less than 1 in Katrina's number line is [tex]\frac{3}{8}[/tex]
2. A point greater than 1 in Eric's number line is 1[tex]\frac{1}{4}[/tex]
What is a number line and how do you identify point less or greater than 1?A number line is a straight line with numbers placed at equal distances from each other.
To identify a line less than 1 in a number line divided into 8, we need to know the value of what each point would be
Each values in Katrina's number line should be 0, [tex]\frac{1}{8}[/tex], [tex]\frac{2}{8}[/tex] , [tex]\frac{3}{8}[/tex], [tex]\frac{4}{8}[/tex], [tex]\frac{5}{8}[/tex], [tex]\frac{6}{8}[/tex], [tex]\frac{7}{8}[/tex] 1
To identify the line greater than 1 in a number line divided into 4, we need to know the values of what each points would be
Each values in Eric's number line should be 1, 1[tex]\frac{1}{4}[/tex], 1[tex]\frac{2}{4}[/tex], 1[tex]\frac{3}{4}[/tex], 2
Check the images below to get a proper view of how your number line should look like.
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Porter is visiting India and would like to purchase some local spices. He finds some spices that cost 320.38 rupees. If the current exchange rate is 1 dollar:73.6500 rupees, how much do the spices cost in U.S. dollars?
$0.04
$4.35
$22.99
$23,595.99
Answer: $4.35
Step-by-step explanation:
320.38 rupees / 73.6500 rupees = $4.35
7) 83÷9 = That I put que pongo
50 points! Compare the triangles and determine whether they can be proven congruent, if possible, by SSS, SAS, ASA, AAS, or HL. Write your answer in the box.
Answer:
1. ASA
2.SSS
3. AAS
4. HL
5. it cannot be proven congruent (not satisfy any criteria)
6. ASA (the top angle of each triangle are congruent)
7. SAS
8. SSS
9. HL
10. AAS
11. it cannot be proven congruent (not satisfy any criteria)
12. SAS or AAS or ASA (the three angles of each triangle are congruent)
Step-by-step explanation:
In the picture attached, the triangles are shown. The criteria are:
SSS: side side side
SAS: side angle side
ASA: angle side angle
AAS: angle angle side
HL: hypotenuse-leg (only valid for right triangles)
two numbers sum 20 difference of 9
Answer: 14.5 and 5.5
Step-by-step explanation:
The issue is using whole numbers. 14+6=20, but 14-6=8. 15+5=20, but 15-5=10. If we use decimals, we can get in between the numbers a little to get 9. 14.5+5.5=20, but unlike 14+6, 14.5 gives 5 a tiny boost to push it to 14.5-5.5=9. Hope that helps!
Answer:
14.5
5.5
Step-by-step explanation:
14.5+5.5=20
14.5-5.5=9
Nine times the input minus seven is equal to the output. Which of the following equations describes this function?
7x-9=y
9y-7=x
9x-7=y
7y-9=x
An equation that describes this function include the following: C. 9x - 7 = y.
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.
This ultimately implies that, an input value (x-value) represents the value on the x-axis of a cartesian coordinate while a output value (y-value) represents the value on the y-axis of a cartesian coordinate.
Based on the information provided, an equation that models the situation is given by;
9x - 7 = y.
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According to the scale on a map, 1 inch on the map = 12 miles. How many miles are represented by 2.5 inches on the map?
Answer:
30 miles
Step-by-step explanation:
(12 miles/inch)(2.5 inches) = 30 miles
9-65 Eric set up this ratio for two similar triangles:
x/12 = 5/9
He solved the problem and found x = 6.67. What was his mistake? What does x REALLY equal?
Eric made the wrong ratio of the sides of the triangle. As corresponding sides of both triangles are in proportion to each other. So, the proportion will be x/12=9/5. x equal to 21.6.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. If the corresponding sides and angles of two triangles are proportionate, then the triangles are similar. As a result, using another triangle, we may determine the dimensions of one triangle.
So, the right ratio of the sides of the triangle is x/12=9/5
12 * 9 / 5 =x
108/5 = x
21.6 = x
Therefore, x is equal to 21.6
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Mathilde has 30 pints of green paint. She uses 3/5 of it to paint a landscape and 3/10 of it while painting a clover. She decides she that, for her next painting, she will need 16 pints or green paint. How much more green paint will she need to buy?
Answer: 13 pints
Step-by-step explanation:
she used 27 pints at first (9/10 of the 30)
so she has 3 pints left.
and 16-3 = 13 pints.
Jevonte mowed 6 lawns in 4 hours. What was his rate of mowing in lawns per hour?
Jevonte's rate of mowing is 1.5 lawns per hour.
How do rates work?A rate in mathematics is an indicator of how one quantity has changed in relation to another, usually given as a ratio or fraction. Rates are frequently used to explain the relationship between two quantities as they vary through time, space, or another variable. For instance, whereas interest rates track the evolution of money over time, speed tracks the change in distance per unit of time. Rates are used to describe and study numerous phenomena in several disciplines, including physics, economics, and finance.
Given that, Jevonte mowed 6 lawns in 4 hours.
Thus,
Rate of mowing = Number of lawns / Number of hours
Rate of mowing = 6 lawns / 4 hours
Rate of mowing = 1.5 lawns per hour
Hence, Jevonte's rate of mowing is 1.5 lawns per hour.
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Hello, can someone help me figure out the standard deviation of this chart?
Answer:
Below
Step-by-step explanation:
I think statistically that all of the scores will fall within 6 standard deviations ..... 3 above the mean and 3 below the mean
from 85 to 165 is 3 standard deviations
165 - 85 = 80 80 / 3 = 26.67 = standard deviation
Hmm.....not sure how they get the S.D. is 40 ....hope someone else can help us !
Standard bellcurve below.... score 125 does not seem to be in the 1 S.D. position of the curve....Kinda close I guess....
Maybe they are saying from 80 to 165 is TWO Standard deviations....THAT would equal 40.....what have your lessons been using?
Please I need help. I don’t understand this. It keeps saying I’m getting the answer wrong but I don’t know what I am doing wrong.
Step-by-step explanation:
This figure is made up of a cone and a semi sphere. Let's find the area of the cone
Volume of a cone
[tex] \frac{1}{3} \pi {r}^{2} h[/tex]
The height is 34 cm.
The radius is half the diameter of the sphere ,
this the radius is 14
[tex] \frac{1}{3} \pi( {14}^{2} )(34)[/tex]
Hint: Do not round mid calculations, only when you are done.
Volume of the semi sphere is
[tex] \frac{1}{2} ( \frac{4}{3} \pi {r}^{3} )[/tex]
The radius is 14
[tex] \frac{1}{2} ( \frac{4}{3} \pi(14) {}^{3} )[/tex]
Add both areas
[tex] \frac{1}{3} \pi( {14}^{2} )(34) + \frac{2}{3} \pi(14) {}^{3} [/tex]
Use 3.14 for pi
Which gives us
12719 to the nearest whole number
9. Zola solved a question on her math test that. asked her to find the volume of the sphere shown
below in terms of T. Explain Zola's error and solve for the correct answer.
d=11 in
v-(-X5.5¹)
V=((16.5)
V = 22π in³
if d=11 in then the volume of the sphere=697.19
[tex]V=\frac{4}{3} \pi d[/tex]
[tex]V=\frac{4}{3} *\frac{22}{7} *5.5^{3} =697.19[/tex]
The amount of room a spherical occupies inside is its volume. Because every point on the sphere's surface is equally spaced from its center, the sphere can be considered a three-dimensional round solid object. The fixed point and fixed distance, respectively, represent the sphere's center and radius. V = 4/3 r3, where r is the radius and V is the volume, is the formula for a sphere's volume. The radius of a sphere is equal to half its diameter. A circle and a sphere are both round, if you compare them. As the sphere is a three-dimensional object rather than a two-dimensional circle, we can estimate its volume and surface area.
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Question 1 of 24
In right -angled triangle, the base is 9 centimeters long and the height is 12 centimeters long. What is the measure of the hypotenuse of the triangle?
The measure of the hypotenuse of the triangle is 15 cm.
What is a hypotenuse?The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle.
Given that, in a right-angled triangle, the base is 9 centimeters long and the height is 12 centimeters long. we need to find the measure of the hypotenuse of the triangle
Using the Pythagoras theorem,
9² + 12² = h²
h² = 81+144
h² = 225
h = 15
Hence, the measure of the hypotenuse of the triangle is 15 cm
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