The algebraic expression for Desmond's height is x + 5.
write an algebraic expression for Desmond's height.If we let "x" represent Niki's height in inches, then Desmond's height can be represented by "x + 5", since Desmond is 5 inches taller than Niki.
So the algebraic expression for Desmond's height is x + 5.
What are algebraic expression?Algebraic expressions is consist of variables, numbers, and mathematical operations (such as addition, subtraction, multiplication, and division).
They can contain one or more variables and can be evaluated for different values of the variables.
For example, the expression 3x + 5y - 2z is an algebraic expression that contains three variables (x, y, and z) and three coefficients (3, 5, and -2) that are multiplied by those variables. Algebraic expressions are commonly used in algebra to represent mathematical relationships and solve problems.
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Find the coordinates of the vertex given the focus and directrix.
focus: (−5,7)
directrix: y=1
lakewood children's Theater started a summer program last year with 245 students. thanks to some advertising during the off-season, 294 students have enrolled this year. the theater will continue this advertising strategy in hopes that enrollment will continue to increase. write an exponential equation in the form y = a(b) that can model the number of enrolled students, y, x, years after the program began.
To model the number of enrolled students, y, x years after the program began, we can use an exponential equation in the form:
y = ab^x
where a is the initial number of students, b is the growth factor, and x is the number of years after the program began.
We are given that the initial number of students was 245, and that the number of enrolled students after one year is 294. Therefore, we can use these values to find the growth factor b:
294 = 245b^1
b = 294/245
b = 1.2
Now that we know the growth factor, we can write the exponential equation in the form y = a(1.2)^x:
y = 245(1.2)^x
This equation can be used to model the number of enrolled students, y, x years after the program began, assuming that the advertising strategy continues to be successful and the growth rate remains constant.
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[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]
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A survey of 100 male diabetic patient and 100 female diabetic students revealed that 15 of the male and 36 of the female were more that 20% overweight. Prepare a contingency table and test the hypothesis that the two gender are homogenous with respect to being overweight (use a= 0,05).
Answer:
Step-by-step explanation:
| Male | Female | Total
------|------|--------|-------
Overweight | 15 | 36 | 51
Not Overweight | 85 | 64 | 149
------|------|--------|-------
Total | 100 | 100 | 200
Now, we can test the hypothesis that the two genders are homogeneous with respect to being overweight using a chi-square test. The null hypothesis is that there is no association between gender and overweight status.
The formula for the chi-square test is:
χ² = Σ [(O - E)² / E]
Where:
χ² = chi-square value
O = observed frequency
E = expected frequency
To calculate the expected frequency, we can use the formula:
E = (row total x column total) / grand total
Using this formula, we can calculate the expected frequencies for each cell of the contingency table:
| Male | Female | Total
------|------|--------|-------
Overweight | 12.75 | 38.25 | 51
Not Overweight | 87.25 | 61.75 | 149
------|------|--------|-------
Total | 100 | 100 | 200
Now we can use the formula for the chi-square test to calculate the chi-square value:
χ² = [(15 - 12.75)² / 12.75] + [(36 - 38.25)² / 38.25] + [(85 - 87.25)² / 87.25] + [(64 - 61.75)² / 61.75]
χ² = 1.06 + 0.76 + 0.68 + 0.56
χ² = 3.06
Next, we need to determine the degrees of freedom (df) for our test. For a contingency table with r rows and c columns, the degrees of freedom are (r-1) x (c-1). In this case, we have 2 rows and 2 columns, so our degrees of freedom are:
df = (2-1) x (2-1) = 1
We can then use a chi-square distribution table or a statistical software program to determine the critical value of chi-square for our chosen level of significance and degrees of freedom. For a significance level of 0.05 and 1 degree of freedom, the critical value of chi-square is 3.84.
Since our calculated chi-square value of 3.06 is less than the critical value of 3.84, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that there is a significant association between gender and overweight status among diabetic patients.
Help me out asap please.
Step-by-step explanation:
4x²+32=4(x²+8)
56x³+7x²=7x²(8x-1)
6x⁴-4x²+14x=2x(3x³-2x+7)
18x³+27x-9=9(2x³+3x-1)
Please help me with this show your work.
Answer:
(2,3)
Step-by-step explanation:
look at where both lines intersect
2x - 1 = 5 - x
Combine like terms
2x + x = 3x
5 + 1 = 6
3x = 6
6 /3 = 2
X = 2
Put into both equation to find y and to make sure it’s true
Y =2x - 1
2(2) - 1
4 - 1 = 3
Y = 3
y = 5 - x
5 - 2 = 3
Y = 3
X=2 and y = 3
(2,3)
To solve a system of equations, we need to find the values of the variables that make both equations true simultaneously. Several methods for solving systems of equations include substitution, elimination, and graphing.
Substitution method:
Solve one equation for one variable in terms of the other variable.Substitute the expression obtained in step 1 into the other equation in place of the variable just solved for.Solve the resulting equation for the remaining variable.Substitute the value obtained in Step 3 back into either of the original equations to find the value of the other variable.Elimination method:
Multiply one or both equations by constants so that the coefficients of one of the variables are equal in both equations, but have opposite signs.Add the resulting equations together to eliminate one of the variables.Solve the resulting equation for the remaining variable.Substitute the value obtained in Step 3 back into either of the original equations to find the value of the other variable.Graphing method:
Graph both equations on the same set of axes.The solution to the system of equations is the point(s) where the two lines intersect.Let's solve this using substitution and then verify with the graphing method:
To solve the system of equations y = 2x - 1 and y = 5 - x, we can substitute the expression 2x - 1 for y in the second equation and solve for x:
y = 5 - x
2x - 1 = 5 - x (substituting y = 2x - 1 for y)
3x = 6
x = 2
Now that we have found x = 2, we can substitute this value into either equation to solve for y:
y = 2x - 1
y = 2(2) - 1
y = 3
We can verify this with the graphing method by looking at where the two lines intersect. Upon inspecting the graph, the lines intersect at (2,3), verifying that the algebraic method was correct. Therefore, the solution to the system of equations is (2,3)
During a physics experiment, a student determines that the unit rate for a marble’s motion is 2 centimeters per second. What is the unit rate describing the number of seconds it takes the marble to travel one centimeter?
100 points !
Answer:
To find the unit rate describing the number of seconds it takes the marble to travel one centimeter, we need to invert the given unit rate of 2 centimeters per second. Inverting the unit rate means swapping the numerator and denominator of the fraction to get a new fraction with the same value but different units.
2 centimeters/second = 1/2 seconds/centimeter
Therefore, the unit rate describing the number of seconds it takes the marble to travel one centimeter is 1/2 seconds/centimeter. This means that it takes the marble half a second to travel one centimeter.
Four increased by three times a number what’s the expression??
Answer:
Th expression would be 3x+4
$-3\left|x\right|+2x-1\:if\:x\:=\:-5$
Answer: = -26
Step-by-step explanation:
Using system of equations
Answer: x = 2 and y = - 4 or (2,-4)
Step-by-step explanation:
Subtract the x from both sides of the equation Now you have y = - x - 2 plug in - x - 2 into the other equationNow you have y = 5x - 3 ( - x - 2) = 22simplify that to 5x + 3x + 6 = 22simplify that to 8x = 16Now x = 2plug in x as 2 into y + x = -2Now y + 2 = -2Subtract the 2 from both sides of the equationNow you have y = - 44) A blueprint for a building has a scale of 1:40 (blueprint:actual). A wall in the blueprint is 4 inches tall. What is the height of the actual wall (in inches)?
*
40 inches
80 inches
1/160th of an inch
160 inches
[tex]\begin{array}{ccll} blueprint&actual\\ \cline{1-2} 1 & 40\\ 4& h \end{array} \implies \cfrac{1}{4}~~=~~\cfrac{40}{h} \implies h=160[/tex]
Answer:
160 inches
Step-by-step explanation:
a scale of 1:40 means that any measurement in the blue print is multiplied by 40 to find the actual measurement
so 4*40= 160 inches
Suppose the temperature in degrees Celsius over an 8-hour period is given by T(T)= ? + 4 t+ 32.
a) Find the average temperature.
b) Find the minimum temperature.
c) Find the maximum temperature.
the average temperature over the 8-hour period is 47°C, the minimum temperature is 32°C, and the maximum temperature is ? + 60°C
a) The average temperature can be found by integrating T(t) from 0 to 8 and dividing by the interval of integration:
Average temperature = (1/8) ∫T(t)dt from 0 to 8
= [tex](1/8) [∫(? + 4t + 32)dt from 0 to 8]= (1/8) [(?t + 2t^2 + 32t) from 0 to 8]= (1/8) [(?8 + 2(8)^2 + 32(8) - (?0 + 2(0)^2 + 32(0)))][/tex]
= (1/8) [(?8 + 128 + 256)]
= (1/8) [376]
= 47°C
Therefore, the average temperature over the 8-hour period is 47°C.
b) The minimum temperature occurs when the derivative of T(t) is equal to 0:
d/dt(T(t)) = 4
Setting this equal to 0, we find that the minimum temperature occurs at t = 0.
Therefore, the minimum temperature over the 8-hour period is T(0) = ? + 4(0) + 32 = 32°C.
c) The maximum temperature occurs when the derivative of T(t) is equal to 0:
d/dt(T(t)) = 4
Setting this equal to 0, we find that the maximum temperature occurs at t = 8.
Therefore, the maximum temperature over the 8-hour period is T(8) = ? + 4(8) + 32 = ? + 60°C.
In summary, we have found that the average temperature over the 8-hour period is 47°C, the minimum temperature is 32°C, and the maximum temperature is ? + 60°C. These results are useful in determining the overall temperature trend and can inform decisions related to temperature regulation or outdoor activities that may be influenced by the temperature.
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How do I solve this system of linear equations
The solution for the system of linear equations is: x₁ = -1, x₂ = -3, x₃ = 3 and x₄ = -2
How do you solve for the system of linear equations?To solve this system of linear equations, we can use the Gaussian elimination method. First, let's represent the system as an augmented matrix:
| 1 0 2 0 | 5 |
| 0 1 0 -1 | -1 |
| -1 -1 1 0 | 1 |
| 0 0 2 -1 | 4 |
Add the first row to the third row to eliminate x₁ in the third row:
| 1 0 2 0 | 5 |
| 0 1 0 -1 | -1 |
| 0 -1 3 0 | 6 |
| 0 0 2 -1 | 4 |
Add the second row to the third row to eliminate x₂ in the third row:
| 1 0 2 0 | 5 |
| 0 1 0 -1 | -1 |
| 0 0 3 -1 | 5 |
| 0 0 2 -1 | 4 |
Divide the third row by 3
| 1 0 2 0 | 5 |
| 0 1 0 -1 | -1 |
| 0 0 1 -1/3 | 5/3 |
| 0 0 2 -1 | 4 |
Subtract twice the third row from the fourth row to eliminate x₃ in the fourth row
| 1 0 2 0 | 5 |
| 0 1 0 -1 | -1 |
| 0 0 1 -1/3 | 5/3 |
| 0 0 0 -1/3 | 2/3 |
Multiply the fourth row by -3 to get x₄
| 1 0 2 0 | 5 |
| 0 1 0 -1 | -1 |
| 0 0 1 -1/3 | 5/3 |
| 0 0 0 1 | -2 |
We can use back substitution to find the values of x₁, x₂, and x₃:
x₄ = -2
x₂ - x₄ = -1 which is x₂ = -1 + (-2) = -3
x₃ - (1/3)x₄ = 5/3 therefore; x₃ = 5/3 + (1/3)(-2) = 3
x₁ + 2x₃ = 5 therefore; x₁ = 5 - 2(3) = -1
The above answer is in response to the full question below;
Solve this system of linear equations
x₁ + 2x₃ = 5
x₂ - x₄ = -1
-x₁ - x₂ + x₃ = 1
2x₃ - x₄ = 4
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Please help! Will give brainliest
[tex]1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}[/tex]
we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.
Alice’s chicken coop (cage) has a total volume of 758 cubic feet (ft3). Use the fact that 1 foot is approximately equal to 0.3048 m to convert this volume to m3.
the volume of Alice's chicken coop in cubic meters is approximately 21.46 m³.
what is volume ?
Volume refers to the amount of space that an object or substance occupies in three-dimensional space. It is typically measured in cubic units, such as cubic meters (m³) or cubic feet (ft³), and is calculated by multiplying the length, width, and height of the object
In the given question,
To convert 758 cubic feet to cubic meters, we need to use the conversion factor:
1 ft³ = 0.3048³ m³
We can then multiply the volume in cubic feet by this conversion factor to get the volume in cubic meters:
758 ft³ × (0.3048 m/ft)³ = 21.46 m³ (rounded to two decimal places)
Therefore, the volume of Alice's chicken coop in cubic meters is approximately 21.46 m³.
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Adjacent side = 26 cm
Hypotenuse = 53 cm
Opposite side =__
Using the Pythagorean theorem, we know that:
hypotenuse^2 = adjacent side^2 + opposite side^2
Substituting the given values, we have:53^2 = 26^2 + opposite side^2
Solving for the opposite side, we get:opposite side^2 = 53^2 - 26^2
opposite side^2 = 2025
opposite side = √2025
opposite side = 45
Therefore, the length of the opposite side is 45 cm.
Verification :The calculation is correct. You can also use the trigonometric ratio of sine to calculate the opposite side. In this case, sinθ = opposite side / hypotenuse, where θ is the angle opposite to the opposite side.
Using the values given, sinθ = opposite side / hypotenuse = opposite side / 53. We can rearrange the formula to get:opposite side = sinθ x hypotenuse
To find θ, we can use the inverse sine function or arcsine. So, sinθ = opposite side / hypotenuse becomes:θ = sin^-1 (opposite side / hypotenuse)
θ = sin^-1 (26/53)
θ = 30.96 degrees
Substituting the values into the formula, we get:opposite side = sinθ x hypotenuse
opposite side = sin(30.96) x 53
opposite side ≈ 45
Therefore, the length of the opposite side is approximately 45 cm, which is the same as our previous calculation.
Pls help me last question on math I got to finish the packet
A reservoir is 60% filled with liquid. It holds up to 1690 gallons how many gallons of water are needed to fill the reservoir to the top?
A reservoir is 60% filled with liquid. It holds up to 1690 gallons so, we need to add 676 gallons of water to fill the reservoir to the top.
The reservoir is already 60% filled, which means it contains 60% of 1690 gallons:
60% of 1690 = 0.6 x 1690 = 1014 gallons
To fill the reservoir to the top, we need to add the remaining 40% of the capacity. We can calculate this by subtracting the current amount of water from the total capacity of the reservoir:
100% - 60% = 40%
40% of 1690 = 0.4 x 1690 = 676 gallons
Therefore, we need to add 676 gallons of water to fill the reservoir to the top.
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Explain how to solve the equation.
C / 9 = 9
Response Please.
Answer: To solve the equation C/9 = 9, you want to isolate the variable C. To do this, you can multiply both sides of the equation by 9 (the denominator of the fraction):
Example: C/9 × 9 = 9 × 9
On the left side of the equation, the 9's cancel out, leaving you with just C:
C = 81
Therefore, the answer to C / 9 = 9 is 81.
Step-by-step explanation: Sincerely, answered by Lizzy ♡ :: as an A+ student, I want to make sure other students can succeed as well, so in my free time: i answer questions like yours on Brainly! if you could click the thanks heart, give me brainliest by clicking the crown, and rate my answer 5 stars, it would be appreciated! have a lovely day! (ᵔᴥᵔ)
Sample Response: Solve by undoing the division by multiplying by 6 on both sides of the equation. The solution is c = 54. Check the solution by substituting 54 for the variable in the original equation and then simplify. 9 = 9 is true, so 54 is the solution.
What is the range of the following relation?
The range of the following relation is -4.5 < y ≤ 2.5
Given data ,
Let the range of the function be represented as R
Now , the value of R is
R = possible output values
And , range is the set of outputs of a relation or function. In other words, it's the set of possible y values.
So , the possible values of "y" are greater than -4.5 (denoted by the symbol "<") and less than or equal to 2.5 (denoted by the symbol "≤")
Hence , the range is -4.5 < y ≤ 2.5
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Can someone help me with this? very much appreciated!!
The answer options are {x | 2 < x < 9}, {y | 0 < y < 7}, {y | 0 ≤ y ≤ 7}, {x | 2 ≤ x ≤ 9}
Reason:
The domain is the set of allowed x inputs.
We look at the x coordinates of the endpoints.
The left-most point is when x = 2.
The right-most point is when x = 9.
The set of x values span between 2 and 9, including each endpoint. So we would say 2 ≤ x ≤ 9
a cylinder and a cone have the same radius and the same volume. the height of the cone is 18 cm. what is the height of the cylinder
Answer:
the height of the cylinder is 6 cm.
Step-by-step explanation:
Let's start by using the formulas for the volume of a cylinder and a cone:
Volume of a cylinder = πr^2h
Volume of a cone = (1/3)πr^2h
Given that the cylinder and cone have the same radius and volume, we can set their volume equations equal to each other:
πr^2h = (1/3)πr^2(18)
Simplifying this equation by canceling out πr^2 on both sides, we get:
h = (1/3) * 18
h = 6
Therefore, the height of the cylinder is 6 cm.2
8. Cassie has some flowers. Each of the flowers are either ORANGE or YELLOW.
One fifth of the flowers are ORANGE. She has 25 ORANGE flowers. How many
YELLOW flowers does Cassie have? Show your work below. [2 points]
Cassie has a total of 100 yellow flowers.
Proportion calculationGiven that one-fifth of the flowers are orange, a proportion can be used to find out how many flowers Cassie has in total.
Assuming x represent the total number of flowers Cassie has:
1/5 = 25/x1 * x = 5 * 25x = 125So Cassie has 125 flowers in total.
If 25 of them are orange, then the remaining flowers must be yellow:
125 - 25 = 100
Therefore, Cassie has 100 yellow flowers.
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The ages of a group of lifeguards are listed.
17, 17, 18, 19, 22, 23, 25, 27, 32, 38
If another age of 18 is added to the data, how would the mean be impacted?
A The mean would stay the same value of about 22.5.
B The mean would stay the same value of about 23.8.
C The mean would increase in value to about 25.6.
D The mean would decrease in value to about 23.3.
Answer: (D): The mean would decrease in value to about 23.3
Step-by-step explanation:
Step 1: Find the Original Mean
Mean = Sum/# of Numbers
Mean = 17 + 17 + 18 + 19 + 22 + 23 + 25 + 27 + 32 + 38/ 10 numbers
Mean = 238/10
Mean = About 23.8
Step 2: Add 18 to the original sum, divide that by 11 numbers
Mean = 238 + 18/11 numbers
Mean = 256/11
Mean = About 23.3
And so, Answer Choice (D) is correct
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
20,10,5,...
Find the 9th term.
Answer:9th term is 0.078 approx.
Step-by-step explanation: the given sequence is decreasing by a factor of 2 each time.
so we can find 4th term :-
4th term= 5/2=2.5
similarly,we can find the term 5th,6th,7th,8th terms respectively:-
5th = 2.5/2=1.25
6th=1.25/2=0.625
7th=0.625/2=0.3125
8th=0.3125/2=0.15625
so 9th term is equal to 0.078.
Y and X can both be proportional if:
A. product is constant
B. quotient is constant
C. increase by x + 2
D. increase by 2x
Y and X can both be proportional if:
A. product is constant
B. quotient is constant
C. increase by x + 2
D. increase by 2x
Answer:
B
Step-by-step explanation:
Help please 20 point asap
please help my homework is hard and i missed a lot of school
The integers that represent each situation are 35, -40, -12, -288, 14, 75, 0, and -95.
We have,
An integer is a whole number that can be positive, negative, or zero but does not include any fractions or decimals.
Examples of integers include -3, 0, 7, and 100.
Now,
You earn $35 for cleaning the neighbour's yards = $35
A scuba diver is 40 feet below sea level = -40 feet
Weight loss of 12 pounds = -12
The temperature on Saturday was 288 degrees below zero degrees.
= -288 degrees
Your team gains 14 points in a game.
= 14
Deposit of $75
= $75
Sea level.
= 0
Withdrawal of $95.
= - $95.
Thus,
The integers that represent each situation are 35, -40, -12, -288, 14, 75, 0, and -95.
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what fraction of prism's volume will be filled by th sand
The fraction of prism with dimensions length=10cm , width= 5cm and height=5cm , made using two cubes of 5cm sides each filled with sand is [tex]\frac{3}{5}[/tex]
What is a prism?
A three-dimensional solid shape or figure known as a prism has two ends that are identical or flat. Prisms are made up of equal cross-sections, flat faces, and congruent bases. The remaining faces of prism are parallelograms or rectangles. Another name for the rectangular prism is a cuboid.
Given that prism if formed using two identical cubes of side 5cm each. The prism so formed using two cubes will be a cuboid also known as rectangular prism.
Dinemsions of prism:
Length=5+5 { length of two cubes}
=10 cm.
width= 5cm {width of one cube}
height=5 cm {height of one cube}
Volume of cuboid= Lengthx widthx height
=10 . 5 . 5
=250 cu. cm
Given that 150 cu. cm volume of prism is filled with sand.
Fraction of volume filled with sand =[tex]\frac{volume of sand}{total volume of prism}[/tex]
=[tex]\frac{150}{250}[/tex]
=[tex]\frac{15}{25}[/tex]
=[tex]\frac{3}{5}[/tex]
Fraction of volume filled with sand =[tex]\frac{3}{5}[/tex]
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Refer to the attachment for the complete question.
DON'T SOLVE IT
I know the answer. I just need to know the TOPIC in geometry.
What is the topic???
Answer:
Triangles in Geometry
Step-by-step explanation:
An album has 15 songs. You make a playlist by randomly shuffling the order of the songs. Which values represent the probability that the first 3 songs in the playlist are the first 3 songs on the album in any order?
This probability is approximately equal to [tex]1.07 * 10^-10.[/tex]
The total number of possible ways to arrange the 15 songs is 15!, which is a very large number. To find the probability that the first 3 songs in the playlist are the first 3 songs on the album in any order, we need to find the number of ways to arrange the first 3 songs on the album and divide it by the total number of possible arrangements.
Since the first 3 songs can be arranged in any order, we can use the permutation formula to find the number of ways:
P(3,3) = 3!
P(3,3) = 6
So there are 6 ways to arrange the first 3 songs on the album.
The total number of possible arrangements of all 15 songs is 15!, as mentioned earlier.
Therefore, the probability that the first 3 songs in the playlist are the first 3 songs on the album in any order is:
6 / 15!
This probability is a very small number, approximately equal to [tex]1.07 * 10^-10.[/tex]
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