the edges of a cube increase at a rate of 5 centimeters per second. The surface area is changing at a rate of 150 cm²/sec.
To calculate the rate at which the surface area of a cube is changing when each edge is 10 cm long, we first need to calculate the surface area of the cube. The surface area of a cube can be calculated by multiplying the length of one edge cubed by 6. In this case, the length of one edge is 10 cm, so the surface area of the cube is 600 cm². Since the edges of the cube are increasing at a rate of 5 cm/sec, the rate at which the surface area of the cube is changing is equal to the surface area multiplied by the rate of increase, or 600 cm² * 5 cm/sec = 300 cm²/sec.
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what is the probability that the number of systems sold is within 1 standard deviation of its mean value?
The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.
Explain the term Discrete Variable?The term "discrete variable" refers to a variable that has a finite range of possible values. such as using only integer numbers. For instance, the total number of students in a class, the quantity of faulty goods in a batch, etc.The given data is
x 1 2 3 4 5 6 7 8
p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01
(a) calculate mean value of x:
μ = E(x)
= ∑(xi.P(xi))
= 4.13
(b) calculate variance of x:
σ² = ∑(xi - E(x))².P(xi)
= 1.81331
(c) calculate standard deviation of x:
σ = √σ²
σ = √1.831
σ = 1.3539
The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:
P(μ - σ < x < μ + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)
= P(2.7761 < x < 5.4839)
= P(x = 3) + P(x = 4) + P(x = 5)
= 0.13 + 0.30 + 0.31
= 0.74
Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.
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The complete question is-
Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.
x 1 2 3 4 5 6 7 8
p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01
What is the probability that the number of systems sold is within 1 standard deviation of its mean value?
A manufacturing company produces 380 units per day currently. The company's goal is to increase the number of units manufactured per day by 30 each year. If the company meets its goal, how many units will it be producing per day 4 years from now?
Answer:
500
Step-by-step explanation:
You want to know the rate in 4 years if it is 380 units per day, and increasing by 30 units per day per year.
RateThe rate in 4 years will be the sum of the current rate and the amount of increase. The amount of increase is the rate of increase, multiplied by time:
amount of increase = (30 units/day)/year × (4 years) = 120 units/day
Then the rate in 4 years will be ...
new rate = current rate + increase
new rate = 380 units/day + 120 units/day = 500 units/day
The company will be producing 500 units per day in 4 years.
Select the graph for the solution of the open sentence. Click until the correct graph appears.
5|x| + 3 < 18
Answer:
graph D
Step-by-step explanation:
if x ≥ 0
5x + 3 < 18
5x < 18 - 3
5x < 15
x < 15/5
x < 3
0≤ x < 3
if x < 0
5(-x) < 18 - 3
- 5x < 15
x > 15/-5
x> -3
-3 < x < 0
final solution
-3 < x < 3
Mia' plant grow at an average rate of 5cm each month. When he bought it, it wa 18 cm tall. Select the function that model the relationhip between y, the height of the plant in cm, and x, the time in month that it grow. A. Y = 18x 5
B. Y = 18 5x
C. Y = x 18
D. Y = 23x
The function that models the relationship between plant height (y) and growth time (x) is y = 18 + 5x
The linear equation of two variables
The two-variable linear equation is a solving system for a mathematical problem in which there are two case variables.
In the problem, we get the info that the plant's initial height is 18 cm, meaning this value will not change.
We also get information that the height of the plants increases by 5 cm every month, meaning this value will change over time. If x is the growth time (in months), then the increase in height over time can be written mathematically as 5x.
Based on the two statements above, if y is the plant height (in cm) after x months, then mathematically it can be written as:
y = 18 + 5x
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Here are the scores for two softball teams for seven innings. Each team's total score is the sum of the numbers in its row. Rosie's Riveters beat The Susan Bees by how many runs?
A baseball scoreboard with the points marked for Rosie's riveters versus The Susan bees.
The team of Rosie's Riveters beat the Susan Bees by 3 runs.
What is Addition?Addition is one of the four basic operations of arithmetic's. The other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined.Given are the scores for two softball teams for seven innings.
The total score of Rosie's Riveters will be -
T{R} = 1 + 3 + 4 + 2 + 1 + 0 + 2 = 13
The total score of Susan Bees will be -
T{S} = 0 + 0 + 5 + 3 + 0 + 1 + 1 = 10
Now -
T{R} - T{S} = 13 - 10 = 3
T{R} - T{S} = 3
Therefore, the team of Rosie's Riveters beat the Susan Bees by 3 runs.
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A student takes an exam. The ratio of her right answers to her wrong answers is 11 to 3. Which of the following could describe this situation?
Answer:
She answered 9 wrong and 33 right.
Step-by-step explanation:
Choices:
She answered 9 wrong and 33 right.
She answered 33 wrong and 9 right.
She answers 14 wrong and 22 right.
She answered 22 wrong and 14 right.
11:3 = 22:6 = 33:9 = 44:12 = 55:15 = 66:18 = 77:21 = 88:24 = ...
33 right 9 wrong works.
Answer: She answered 9 wrong and 33 right.
what is the slop of this question
Answer:
slope = 6
Step-by-step explanation:
(0,6)
(1,12)
12-6
-------- = 6
1-0
PLEASE HELP!!!
Ralph and Liza are both driving fro Los Angeles to Santa Fe. Ralph leaves at 7:00 and averages 60 mph (miles per hour) on the way. Liza leaves at 7:25 and averages 65 mph on the way. The situation is modeled by this system, where x is number of hours after Liza leaves and y is the distance each will travel:
y=60x+25
y=65x
How long after Liza leaves will she pass Ralph, and how far will they each have traveled?
A. Liza will not pass Ralph, because she will never catch up with him.
B. Liza will pass Ralph after 3 hours, and they each will have traveled 205 miles.
C. Liza will pass Ralph after 5 hours, and they each will have traveled 325 miles.
D. Liza will pass Ralph after 4 hours, and they each will have traveled 260 miles.
To find the time and distance at which Liza passes Ralph, we need to solve the system of equations.
Subtracting the first equation from the second, we get:
65x - 60x = y - 25
5x = y - 25
y = 5x + 25
Substituting this value of y into the first equation, we get:
60x + 25 = 5x + 25
55x = 0
x = 0
This means that Liza will pass Ralph 0 hours after she leaves, or at the same time as Ralph. At this time, they will have both traveled 0 miles.
Therefore, the answer is A: Liza will not pass Ralph, because she will never catch up with him.
The graph of a proportional relationship is shown. Write an equation that relates Kai’s earnings y, in dollars, to x, the number of hours he works
Answer:y=7.5x
Step-by-step explanation:
In the 9th grade HMH Math book for teachers, it explains that you must divide 150 by 20 and put it in the equation.
how many of your 500 clients would you expect to have major depressive disorder (mdd)? if you used the phq-2 to screen for mdd, what number of those who are depressed would screen positive? among those who screened positive, what number would you expect to be confirmed for mdd at the follow-up visit?
As per the unitary method, the number would you expect to be confirmed for MDD at the follow-up visit is approximately 166.
The term unitary method in statistics refers a basic concept to find the value of a single unit and then using that value to find the value of multiple units.
Here we have to find how many of your 500 clients would you expect to have major depressive disorder and if you used the phq-2 to screen for MDD, what number of those who are depressed would screen positive.
In order to find the number of patients with MDD, we must know the process of PHQ - 2.
The process of PHQ - 2 involves the following steps:
Here the score ranges from 0-6.
And if the score is 3 or greater, then major depressive disorder is likely.
Based on these we have to test the 500 with PHQ test, let us consider that there is 2 person in every two person has MDD.
So, the number of MDD patient is approximately 166.
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4. Choose all the equations that are true
if x = 8.
A. 0²/x = 6/²/
B. x +11.5 = 20.5
C. 23.42 - x = 15.42
D. 11x = 88
E. 40 ÷ x = 6
The equations that are true if x = 8 are:
B. x + 11.5 = 20.5
C. 23.42 - x = 15.42
D. 11x = 88
In equation B, x is equal to 8, so 8 + 11.5 = 20.5, which is a true statement. In equation C, x is also equal to 8, so 23.42 - 8 = 15.42, which is a true statement. In equation D, x is equal to 8, so 11*8 = 88, which is a true statement.
Equation A is not true because the expression 0^2/x is undefined, since division by zero is not allowed. Equation E is not true because 40 ÷ 8 is equal to 5, not 6.
Answer:
whats f
Step-by-step explanation:
Solve the system of equations using subtraction 4x − 4y = 4 4x + y =19
Answer:
4×-4y=4
-(4x+y=19)
0x -5y=-15
5y=15
y=3
4x-12=4
x=4
Q1)Here is a rectangle It is 8cm and (2b-5)cm
A)Find an expression for the perimeter of the rectangle, in terms of b.
Give your answer in its simplest form.
B) Find the value of b when the perimeter is 42 cm.
In terms of b, the perimeter expression is 6 + 4b and the value of b is 9
How to find an expression for the perimeter of the rectangle,From the question, we have the following parameters that can be used in our computation:
Dimensions = 8cm and 2b - 5 cm
The above parameters mean that
Length = 8
Width = 2b - 5
The perimeter is calculated as
Perimeter = 2 * (Length + Width)
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (8 + 2b - 5)
Evaluate the like terms
Perimeter = 2 * (3 + 2b)
Open the brackets
Perimeter = 6 + 4b
B) Find the value of b when the perimeter is 42 cm.Here, we have
Perimeter = 42
This means that
6 + 4b = 42
So, we have
4b = 36
Divide by 4
b = 9
Hence, the value is 9
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Mr. Gonzale howed tudent part of the prime factorization of 90. One factor i miing. Write the number that complete thi prime factorization?
Given the prime factorization of 90. The number that complete thi prime factorization is 2 × 3² × 5.
Determine the prime factorization of 90Factor tree
90
/\
2 45
/\
3 15
/\
3 5
The prime factorization
90 = 2 × 3 × 3 × 5
= 2 × 3² × 5
So, the number that complete thi prime factorization is 2 × 3² × 5.
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someone help me please
Answer:
Negative
Step-by-step explanation:
Knowledge Needed
The discriminant of a quadratic function is b^2-4ac.
If the discriminant is positive, there are 2 x-intercepts.
If the discriminant is 0, there is 1 x-intercept.
If the discriminant is negative, there are 0 x-intercepts.
Question
If the parabola does not intersect with the x-intercept, the discriminant is negative.
Kane i training for a marathon. He tart running 3 mile during every training eion. Each week he plan to increae the ditance of hi run by 1/4 mile. Let w be the number of week. Write an expreion to how the ditance Kane run in a training eion after w week
The expression to which the distance Kane run in a training session after w week is {3+(1÷4)w}...
Kane is training for a marathon. He start running 3 miles during every training session. Each week he plan to increase the distance of his running by 1/4 miles. Let 'w' be the number of week.
Let w be the number of week.
So the expression is formed as that in 1st week if he sart running 3 miles and after every week 1/4 miles added ,it's mean 1 by forth part of one mile is added after every week so if;
we suppose that we have to calculate it for "w" weeks then these weeks will be multiply with 1/4 and then added to the starting miles which are 3 miles
So the expression will be:
{3+(1÷4)w}
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Your question is may be misspelled it will be...(Kane is training for a marathon. He start running 3 miles during every training session. Each week he plan to increase the distance of his running by 1/4 miles. Let 'w' be the number of week. Write an expression to how the distance Kane run in a training session after 'w' weeks?
Write an equation of the line that passes through (-2, 4) and is perpendicular to y = -2x + 4
Answer:
y=-2x
Step-by-step explanation:
PLEASE HELP!!
Find c.
Round to the nearest tenth:
Answer:48
Step-by-step explanation:
g. 390, 702 and 468 lcm of the following
Answer:
7020
Step-by-step explanation:
2÷390,702,468
2÷195,351,234
3÷
14. If AABC is similar to ADEF, what proportion would be used to solve for 2?
The proportionality used in the given diagram is 4/3=12/x if ΔABC and ΔDEF are similar. So, option 4 is correct.
What is meant by triangle?Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.
In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.
We have to assume that ΔABC and ΔDEF are similar.
If the triangles are similar,
Then the proportionality is:
AB/BC=DE/EF
4/3=12/x
Therefore, the proportionality used in the given diagram is 4/3=12/x.
So, option 4 is correct.
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A store sells both cold and hot beverages. Cold beverages, c, cost $1.50, while hot beverages, h, cost $2.00. On Saturday, drink receipts totaled $360, and 4 times as many cold beverages were sold as hot beverages.
Which system of linear equations represents the beverage sales on Saturday?
4c = h
1.5c + 2h = 360
c = 4h
1.5c + 2h = 360
c + h = 360
1.5c = 4(2h)
c + h = 360
4(1.5c) = 2h
Answer:4c=h
Step-by-step explanation:
The first linear equation, 4c=h
Which statements proved that the two triangles are using the SSS similar theorem?a. its corresponding sides has a proportional ratio of 1/2
b. its corresponding sides has a proportional ration is 1/3
c. its corresponding sides has a proportional ration is 1/4
d. its corresponding sides has a proportional ration is 1/5
Option B is the correct answer. corresponding sides have a proportional ratio is 1/3 of the sss theorem.
If two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional. This is called the SSS Similarity Theorem.
when the three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar, it is also called SSS Similarity Theorem.
SSS Theorem png
If ABYZ=BCZX=ACXY , then ΔABC∼ΔYZX .
Considering triangles have 3 sides, having each side has a 1/3 ratio will make it congruent to the other triangle.
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Hi can you please help me like rnn
js 1 & 2 for now
Step-by-step explanation:
1.
it is always the same.
the usual equation of a line is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y-value when x = 0).
we see that the y-value is +3 when x = 0. that is "b".
for the slope we pick 2 points (with integer coordinates, if possible).
I see e.g. (0, 3) and (3, 0)
x changes by +3 (from 0 to 3).
y changes by -3 (from 3 to 0).
the slope "a" is -3/+3 = -1
the equation is
y = -x + 3
2.
and again the same
we see that the y-value is -3 when x = 0. that is "b".
I see e.g. (0, -3) and (3, 0) as points.
x changes by +3 (from 0 to 3).
y changes by +3 (from -3 to 0).
the slope "a" is +3/+3 = 1.
the equation is
y = x - 3
Sofia ordered sushi for a company meeting. They change plans and increase how many people
will be at the meeting, so they need at least 100 pieces of sushi in total.
and paid for 24 pieces of sushi, so she needs to
Sofia had already ordered
order additional sushi.
The sushi comes in rolls, and each roll contains 12 pieces and costs $8.
Answer: Sofia needs to order an additional 100 - 24 = 76 pieces of sushi.
Since each roll contains 12 pieces, Sofia needs to order 76 / 12 = 6 additional rolls of sushi.
At a cost of $8 per roll, Sofia will need to pay an additional 6 * $8 = $48 for the additional sushi.
Step-by-step explanation:
Can You pls solve this problem
Please quick I’ll give brainliest
one segment measures 161 cm. Calculate its multiple according to the number 3 and its submultiple according to the number 7
Multiple according to the number 3 is 162 and its submultiple according to the number 7 is 7.
What is called 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.
Given that :
One segment measures 161 cm
To find the multiple according to the number 3, divide 161 by 3.
161 ÷ 3 = 53.67
Nearest integer of 53.67 is 54
The multiple according to the number 3 = 54 × 3
= 162
To find the submultiple according to the number 7, divide 161 by 7.
161 ÷7 = 23
Nearest integer of 23 is 23
The submultiple according to the number 7 = 161 ÷ 23
= 7
Multiple according to the number 3 is 162 and its submultiple according to the number 7 is 7.
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Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15.
Find the z-score to the nearest tenth for the following blood pressure readings.
a. 142 -
b. 130 -
c. 103 -
The required values of the z-score as per the corresponding blood pressure readings are: z-score = 1.267 when reading is 142, z-score = 0.6 when reading is 130, and z-score = -1.2- when reading is 103.
What is Z -score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
Normally distributed with a mean of 121 and a standard deviation of 15.
As per the given question, we have
mean ц = 121
standard deviation σ = 15
For X₁ = 140
z-score = (X₁ - ц )/σ
z-score = (140 - 121)/15
z-score = (19)/15 = 1.267
For X₂ = 130
z-score = (X₂ - ц )/σ
z-score = (130 - 121)/15
z-score = (9)/15 = 0.6
For X₃ = 103
z-score = (X₃ - ц )/σ
z-score = (103- 121)/15
z-score = (19)/15 = - 1.2
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You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 44 pieces of clothing (shirt, pants, socks, or hat) and 3 33 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?.
The probability of ending up with an orange hat is 1/12. It is because here are twelve possible outcomes.
What is Probability?Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.
It is represented mathematically as;
Probability = Number of Expected outcomes / Total number of outcomes
From the question, we can have the following outcomes;
Clothing = 4
Colors = 3
Pr (pick a clothing) = 1/4
Pr (pick a color) = 1/3
Pr (picking an orange hat) = 1/4 x 1/3
Pr (picking an orange hat) = 1/12.
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Last year you were 63 inches tall. This year you are 68 inches
tall. What is the percent change from last year to this year?
(Remember to write increase or decrease)
The percent increase from last year to this year is 7.94%
How to determine the percent change from last year to this year?From the question, we have the following parameters that can be used in our computation:
Initial height = 63 inches
New height = 68 inches
The percent change from last year to this year is then calculated as
Percent change = (New height - Initial height)/Initial height * 100%
Substitute the known values in the above equation, so, we have the following representation
Percent change = (68 - 63)/63 * 100%
Evaluate
Percent change = 7.94%
Hence, the percentage increase is 7.94%
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Alda is measuring the growth of a plant. Its initial height was 14 centimeters (cm), and the plant has consistently grown 32 cm each day.
Which linear equation represents the plant height, (y), after a given number of days, (x)?
Responses
y=32x+14y is equal to 3 halves x plus 14
x=32y+14x is equal to 3 halves y plus 14
y=14x+32y is equal to 14 x plus 3 halves
y=32x−14
The linear equation that represents the plant height is the one in the first option:
y = 14 + (3/2)x
Which linear equation represents the height?We know that the initial height of the plant (this will be the y-intercept of the line) is 14cm, and we also know that the plant grows at a rate of 3/2 cm each day.
So, after x days, the plant is x times 3/2cm plus 14 cm of height, so the linear equation is:
y = 14 + (3/2)x
So the correct option is the first one.
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