Hello!
Given,
Perimeter of rectangle = 32 cm
Width = 7cm
Perimeter of a rectangle = 2 (l+b)
32cm = 2l + 2 (7cm)
32 cm = 2l + 14cm
32cm -14cm =2l
2l= 18cm
l = 9cm
Area of a rectangle = length × breadth
= 7cm × 9cm
= 63 cm^2
Find the derivative of the function h(w), below. It may be to your advantage to simplify before differentiating: h(w) = 7w arcsin w h' (w)=
Therefore, the derivative of the function h(w) is h'(w) = [tex]7*arcsin(w) + w*cos(w)*7.[/tex]
The derivative of the function h(w) is h'(w) = [tex]7*arcsin(w) + w*cos(w)*7[/tex]. To find this, first simplify the original function using the identity arcsin(w) = sin-1(w), then use the chain rule. We get:
h'(w) = 7*sin-1(w) + w*cos(sin-1(w))*7
Since sin-1(w) is the inverse of sin(w), we can substitute w for sin(w). This gives us:
h'(w) = 7*sin-1(w) + w*cos(w)*7[tex]7*sin-1(w) + w*cos(w)*7[/tex]
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find the measure of the arc or angle indicated A) 29° B) 39° C) 49° D) 26°
Check the picture below.
auditors compared opinions about treatment (very good/acceptable/poor) at four va hospitals (labeled a,b,c,d) among veterans aged 50 and above. what are the hypotheses for a chi-square test of independence on the data? select one:
The hypotheses for a chi-square test of independence on the data that auditors compared opinions about treatment (very good/acceptable/poor) at four VA hospitals (labeled a,b,c,d) among veterans aged 50 and above are:
Null hypothesis, H0: There is no association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.
Alternative hypothesis, Ha: There is an association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.
Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.
An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.
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sam wants to color the three sides of an equilateral triangle. he has five different colors to choose from. in how many different ways can sam color the sides of the triangle? (two colorings are considered the same if one coloring can be rotated and/or reflected to obtain the other coloring.)
There are 27 different ways for Sam to color the sides of the equilateral triangle, accounting for rotations and reflections.
We have,
To calculate the number of different ways Sam can color the sides of the equilateral triangle, we need to consider the symmetry of the triangle.
Since two colorings are considered the same if one coloring can be rotated and/or reflected to obtain the other coloring, we need to account for these symmetries.
Let's analyze the possibilities:
- All three sides have the same color:
There is only one way to color the triangle in this case.
- Two sides have the same color, and the third side has a different color: Sam can choose the color for the two sides in 5 ways and the color for the remaining side in 4 ways (since it must be different from the other two colors).
However, we need to divide this by 3 to account for the different rotations of the equilateral triangle.
Thus, there are (5 x 4) / 3 = 20 / 3 = 6.67 (approx) ways to color the triangle in this case.
Since the number of colorings must be a whole number, we consider this as 6 ways.
- All three sides have different colors:
Sam can choose the color for the first side in 5 ways, the color for the second side in 4 ways (since it must be different from the first), and the color for the third side in 3 ways (since it must be different from the first two).
However, we need to divide this by 6 to account for the different rotations and reflections of the equilateral triangle.
Thus, there are (5 x 4 x 3) / 6 = 20 ways to color the triangle in this case.
In total, the number of different ways Sam can color the sides of the equilateral triangle is:
= 1 + 6 + 20
= 27.
Thus,
There are 27 different ways for Sam to color the sides of the equilateral triangle, accounting for rotations and reflections.
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a manager recorded the number of gallons of ice cream sold for the past six periods. he asked you to choose a forecasting model to predict the demand for gallons of ice cream in period 7. you consider applying a two-period moving average model and a two-period weighted moving average model with weights of 0.6 and 0.4. a) which model is better for this data set (hint: show all your work including forecasts for each period and calculations using measures of forecast accuracy)? (9 points)
The two-period moving average model and the two-period weighted moving average model are both common forecasting methods used to predict future demand. and we understand that the model with the lower MAD and MSE values will have the most accurate forecast.
To determine which model is better for this particular data set, we need to compare the accuracy of each model. To do this, we will calculate the Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE) for each model.
For the two-period moving average model, we can calculate the forecast for period 7 by taking the average of p5 and 6:
Period 7 forecast = (Gallons in Period 5 + Gallons in Period 6)/2
For the two-period weighted moving average model, we can calculate the forecast for period 7 by using the weights of 0.6 and 0.4:
Period 7 forecast = (0.6 x Gallons in Period 5) + (0.4 x Gallons in Period 6)
We can then compare the accuracy of each model by calculating the MAD and MSE. To calculate MAD, we need to subtract the actual demand in each period from the forecasted demand and take the absolute value:
MAD = |Actual demand – Forecasted demand|
To calculate MSE, we need to square the differences between the actual demand and the forecasted demand:
MSE = (Actual demand – Forecasted demand)^2
After calculating the MAD and MSE for each model, we can compare the results to determine which model is better for this data set. The model with the lower MAD and MSE values will have the most accurate forecast.
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(x-20)²=x²-20 pleas im struggling i need help
Answer:
Step-by-step explanation:
[tex](x-20)^2=x^2-20[/tex]
Expanding LHS gives:
[tex]x^2-40x+400=x^2-20[/tex]
[tex]-40x+400=-20[/tex] (subtracted [tex]x^2[/tex] from both sides)
[tex]-40x=-420[/tex] (subtracted 400 from both sides)
[tex]x=\frac{-420}{-40}[/tex] (divided both sides by-40)
[tex]x=\frac{21}{2} =10\frac{1}{2}[/tex]
Find the area of the cicumfrance of a circle with diameter of 5ft use 3.14 for pi
Step-by-step explanation:
The formula to solve for the area of a circle is given by,
A
=
1
4
π
d
2
where
d
is the diameter.
Substituting the given, we have
A
=
1
4
×
3.14
×
(
3
ft
)
2
=
1
4
×
3.14
×
9
ft
2
A
=
7.065
ft
2
Next, solve for the circumference.
The formula for the circumference of a circle is written as,
C
=
π
d
where
d
is the diameter.
Substituting the given, we have
C
=
3.14
×
3
ft
C
=
9.42
ft
Hence, the
Area
=
7.065
ft
2
and the
Circumference
=
9.42
ft
.
Answer:
A = 19.625 ft²
C = 15.7 ft
Step-by-step explanation:
The equation for the area of a circle is πr², where r is the radius.
The radius is half of the diameter, so the radius here is 2.5.
Plug the radius into the equation and substitute 3.14 for π:
A = 3.14 x 2.5²
2.5² = 2.5 x 2.5 = 6.25
A = 3.14 x 6.25 = 19.625
Area = 19.625 ft²
The equation for the circumference of a circle is 2πr.
Plug the radius into the equation and substitute 3.14 for π:
C = 2 x 3.14 x 2.5
C = 15.7
Circumference = 15.7 feet.
Aamena buys a business costing $23000
She pays part of this cost with $12000 of her own money
Calculate what percentage of the $23000 this is
Show your calculations
Answer:
52.17%
Step-by-step explanation
[tex]\frac{12000}{23000}[/tex] ×100%
[tex]\frac{1200}{23}[/tex]
52.17
A simplified carbon cycle with aerobic and anaerobic processes is depicted here. Although much of the emphasis on global climate change has been on increasing carbon dioxide levels, methane is also a greenhouse gas whose levels are increasing due to human and other activity. Which of these actions would increase methane levels in the atmosphere and potentially affect global climate change? Select ALL that apply.
--------------------------------------------------------------------------------------------------------------------------------
A Agricultural practices in rice cultivation releases methane.Agricultural practices in rice cultivation releases methane.
B Anaerobic digestion of cellulose by cows produces methane.Anaerobic digestion of cellulose by cows produces methane.
C Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.
D Industrial combustion of fossil fuels releases methane into the atmosphere.Industrial combustion of fossil fuels releases methane into the atmosphere.
E Anaerobic decomposition of landfill material releases methane into the atmosphere.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
what is equation ?A mathematical equation is a claim that two expressions are equal, typically represented with an equal sign (=) between them. The terms "left hand side" (LHS) and "right hand side" (RHS) of the equation, respectively, refer to the expressions on either side of the equal sign. Equations are a common tool for problem solving because they may be used to depict relationships between variables or quantities and to determine the value(s) of the unknown variable(s) that satisfies the equation. For instance, the link between the variables x and the integers 2, 5, and 11 is represented by the equation 2x + 5 = 11. Finding the value of x that makes the left and right sides of the equation equal is necessary to solve this equation.
given
A) Rice farming operations release methane into the atmosphere.
B) Methane is created when cows break down cellulose anaerobically.
E) Methane is released into the atmosphere when landfill material decomposes anaerobically.
Any of the aforementioned behaviours would raise the atmospheric methane concentrations and may have an impact on climate change globally.
Methane is a greenhouse gas that causes the atmosphere of the Earth to warm.
It is produced by both natural and artificial processes. Examples of human activities that contribute to methane emissions into the atmosphere include the production of rice, cattle digestion, and landfill decomposition.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
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find the circumference of each circle
Answer:
[tex]\large\boxed{\mathtt{C=100 \pi \ in.}}[/tex]
[tex]\large\boxed{\mathtt{C \approx314.16 \ in.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked for the circumference of this circle.}[/tex]
[tex]\textsf{Let's review what the Circumference of a circle actually is.}[/tex]
[tex]\large\underline{\textsf{What is the Circumference?}}[/tex]
[tex]\textsf{The Circumference is is the length 'on' the circle.}[/tex]
[tex]\textsf{Circumference is the Perimeter of the Circle; The sum of all the curved edges.}[/tex]
[tex]\large\underline{\textsf{How do we find the Circumference?}}[/tex]
[tex]\textsf{To find the Circumference, we should use a common, and simple formula.}[/tex]
[tex]\mathtt{Circumference=(Diameter) \pi}[/tex]
[tex]\textsf{Pi will be multiplied by the Diameter of the Circle.}[/tex]
[tex]\textsf{Because we are given the Diameter, we can start solving for x.}[/tex]
[tex]\large\underline{\textsf{Substitute;}}[/tex]
[tex]\mathtt{Circumference \ (C)=(100 \ in.) \pi}[/tex]
[tex]\large\boxed{\mathtt{C=100 \pi \ in.}}[/tex]
[tex]\large\boxed{\mathtt{C \approx314.16 \ in.}}[/tex]
which of the following was traditionally an assumption underlying the independent samples t-test question 10 options: a) scores must be drawn from a normally distributed population b) variances should be unequal in both groups c) data should be at the nominal level d)all of the above
The assumption underlying the independent samples t-test is that the scores must be drawn from a normally distributed population. Option A is correct.
What is a t-test?A t-test is a statistical method that determines whether two groups of observations are significantly different from one another. When comparing the means of two populations, the t-test is commonly used. The t-test is used to determine whether two groups' means are significantly different when the samples are drawn from normally distributed populations with equal variances.
The t-test is a powerful tool for determining whether a sample is significantly different from a population or whether two samples are significantly different from one another. The independent samples t-test, as opposed to the dependent samples t-test, is a t-test that compares the means of two independent groups. In this situation, the groups are separate and distinct.
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a) Work out the value that completes the equation for the line on the graph. b) If Keira has burned 640 calories cycling, how many miles has she cycled? Give any decimal answers to 2 d.p. x distance cycled Number of calories burned against distance cycled calories burned Calories burned 400 350 300- 250 200 150 100 50 0 2 4 6 8 10 12 14 16 Distance cycled (miles)
The value that completes the equation for the line on the graph is -200. Keira has cycled 44.8 miles if she has burned 640 calories.
What is slope?It describes how much the dependent variable (y) changes for a given change in the independent variable (x).
According to question:a) To work out the value that completes the equation for the line on the graph, we need to find the equation of the line that passes through two points on the graph. Let's choose two points on the line, for example, (8, 250) and (16, 400).
In this case, the change in y is 400 - 250 = 150, and the change in x is 16 - 8 = 8. Therefore, the slope is:
slope = 150 / 8 = 18.75
y - y1 = m(x - x1)
Let's use the point (16, 400):
y - 400 = 18.75(x - 16)
Simplifying this equation, we get:
y = 18.75x - 200
Therefore, the value that completes the equation for the line on the graph is -200.
b) To find the distance cycled if Keira has burned 640 calories, we need to use the equation of the line we found in part (a). We can set y (calories burned) equal to 640 and solve for x (distance cycled):
640 = 18.75x - 200
840 = 18.75x
x = 44.8 (rounded to 2 decimal places)
Therefore, Keira has cycled 44.8 miles (to 2 decimal places) if she has burned 640 calories.
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how many liters of a 25 % 25%, percent saline solution must be added to 3 33 liters of a 10 % 10, percent saline solution to obtain a 15 % 15, percent saline solution?'
Answer:
Here, x represents the amount (in liters) of the 25% saline solution to be added.
We can see that the 25% saline solution needs to be mixed with the 10% saline solution to obtain a mixture that is 15% saline. The ratio of the volumes of the 25% and 10% solutions can be found by subtracting the concentrations of the two solutions and dividing by the difference between the desired concentration and the concentration of the 10% solution:
x / (3.33 - x) = (15 - 10) / (25 - 10) = 5/15 = 1/3
Multiplying both sides by 3.33 - x, we get:
x = (1/3) (3.33 - x)
Multiplying both sides by 3, we get:
3x = 3.33 - x
Solving for x, we get:
x = 0.833 liters
Therefore, 0.833 liters of the 25% saline solution must be added to 3.33 liters of the 10% saline solution to obtain 4.163 liters of a 15% saline solution.
Step-by-step explanation:
Please help me with my math!
Answer:
-3
Step-by-step explanation:
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To rewrite the quadratic equation 9 = -3x^2 -18x - 25 in the form y = a(x - p)^2 + q, we need to complete the square. First, we factor out the leading coefficient of -3:
-[tex]3(x^2 + 6x + 25/3) = -3(x^2 + 6x + 9 + 16/3)[/tex]
Next, we add and subtract 9 inside the parentheses to complete the square:
[tex]-3(x^2 + 6x + 9 - 9 + 16/3) = -3((x + 3)^2 - 1/3)[/tex]
Simplifying the expression further, we get:
[tex]-3(x + 3)^2 + 3 = y[/tex]
Comparing this to the standard form y = a(x - p)^2 + q, we can see that a = -3, p = -3, and q = 3. Therefore, the value of p is -3.
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Answer:
[tex]p = - 3[/tex]Step-by-step explanation:
To find:-
The value of p .Answer:-
We are here given that a quadratic equation is written in the form of y = a(x-p)² + q and we are interested in finding out the value of "p" .
So , the given quadratic equation to us is ,
[tex]\longrightarrow y = -3x^2-18x-25\\[/tex]
Now complete the square on the RHS side of the equation as ,
Firstly make the coefficient of x² as 1 . This can be done by taking out -3 as common.
[tex]\longrightarrow y = -3\bigg(x^2+6x +\dfrac{25}{3}\bigg)\\[/tex]
we can rewrite it as ,
[tex]\longrightarrow y = -3\bigg( x^2+2(3)(x) +\dfrac{25}{3}\bigg) \\[/tex]
Add and subtract 3² , as ;
[tex]\longrightarrow y = -3\bigg( x^2+2(3)(x) + 3^2-3^2+\dfrac{25}{3}\bigg) \\[/tex]
Rearrange the terms as ,
[tex]\longrightarrow y = -3 \left\{ (x^2+2(3)(x) + 3^2) - 9 +\dfrac{25}{3}\right\} \\[/tex]
Notice the terms inside the small brackets are in the form of [tex]a^2+b^2+2ab[/tex] which is the whole square of [tex] (a+b)[/tex] . Hence , we can write it as ,
[tex]\longrightarrow y =-3\bigg\{ (x+3)^2 + \dfrac{-27+25}{3}\bigg\} \\[/tex]
Simplify,
[tex]\longrightarrow y = -3\bigg\{ (x+3)^2 -\dfrac{2}{3}\bigg\} \\[/tex]
Open the curly brackets by multiplying the terms inside the brackets by -3 as ,
[tex]\longrightarrow y = -3(x+3)^2 - 2 \\[/tex]
Now compare it with [tex] y = a(x-p)^2+q [/tex] . On comparing we get ,
[tex]\longrightarrow \boxed{\boldsymbol{ p =-3}}\\[/tex]
Hence the value of p is -3 .
please help me solve this problem
Answer:
549.61
Step-by-step explanation:
5.5*10^2-3.9*10^-1
5.5*100-3.9*0.1
550-0.39
549.61
Answer:
Scientific notation: 5.4961 × 10²
Standard form: 549.61
Step-by-step explanation:
Scientific notation is written in the form [tex]a\times 10^n[/tex], where [tex]1 \leq a < 10[/tex] and [tex]n[/tex] is any positive or negative whole number.
To subtract two numbers in scientific notation, first write the numbers in the same form, with the same exponent (power of 10).
To convert 3.9 × 10⁻¹ so that the base 10 has an exponent of 2, move the decimal point 3 places to the left and add 3 to the exponent:
[tex]\implies 3.9 \times 10^{-1} = 0.0039 \times 10^2[/tex]
Therefore, we now have:
[tex]5.5 \times 10^2 - 0.0039 \times 10^2[/tex]
Factor out the common term 10⁻¹:
[tex]\implies (5.5 - 0.0039) \times 10^2[/tex]
Subtract the numbers:
[tex]\implies 5.4961 \times 10^2[/tex]
The answer has been given in scientific notation. If the answer should be in standard form then:
[tex]\implies 5.4961 \times 10^2=549.61[/tex]
If f(x)=x^3, evaluate f(x+h)-f(x)÷h, Where h* 0. Use your result to find the derivative of f(x) with respect to x. Differentiate with respect to x (x²-3x+5)(2x-7) .Find with respect to x the derivative of sinx ÷1– cosx
Answer:
If f(x)=x^3, evaluate f(x+h)-f(x)÷h, Where h* 0. Use your result to find the derivative of f(x) with respect to x. Differentiate with respect to x (x²-3x+5)(2x-7) .Find with respect to x the derivative of sinx ÷1– cosx
Step-by-step explanation:
We are given f(x) = x^3. We need to find the value of (f(x+h) - f(x))/h.
f(x+h) = (x+h)^3 = x^3 + 3x^2h + 3xh^2 + h^3
Therefore, (f(x+h) - f(x))/h = [x^3 + 3x^2h + 3xh^2 + h^3 - x^3]/h
= 3x^2 + 3xh + h^2
Taking the limit of the above expression as h approaches 0, we get:
lim(h→0) [(f(x+h) - f(x))/h] = 3x^2
Therefore, the derivative of f(x) = x^3 with respect to x is 3x^2.
Next, we need to differentiate (x^2-3x+5)(2x-7) with respect to x.
Using the product rule, we get:
d/dx [(x^2-3x+5)(2x-7)] = (2x-7)(2x-3) + (x^2-3x+5)(2)
Simplifying, we get:
d/dx [(x^2-3x+5)(2x-7)] = 4x^2 - 20x + 11
Therefore, the derivative of (x^2-3x+5)(2x-7) with respect to x is 4x^2 - 20x + 11.
Finally, we need to find the derivative of sin(x)/(1-cos(x)) with respect to x.
Using the quotient rule, we get:
d/dx [sin(x)/(1-cos(x))] = [(1-cos(x))cos(x) - sin(x)(sin(x))]/(1-cos(x))^2
Simplifying, we get:
d/dx [sin(x)/(1-cos(x))] = cosec(x/2)^2
Therefore, the derivative of sin(x)/(1-cos(x)) with respect to x is cosec(x/2)^2.
Find the 8th term of the arithmetic sequence x + 1 x+1, 8 x − 3 8x−3, 15 x − 7 ,
Answer: 50x - 27
Step-by-step explanation:
To find the 8th term of the arithmetic sequence, we need to first find the common difference between consecutive terms:
Common difference (d) = second term - first term
d = (8x - 3) - (x + 1)
d = 7x - 4
Now, we can use the formula to find the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Plugging in the values, we get:
a8 = (x + 1) + (8 - 1)(7x - 4)
a8 = x + 1 + 7(7x - 4)
a8 = x + 1 + 49x - 28
a8 = 50x - 27
Therefore, the 8th term of the arithmetic sequence x + 1, 8x - 3, 15x - 7 is 50x - 27.
Construct a residual plot of the amount of money in a person’s bank account and their age that would indicate a linear model
To construct a residual plot of the relationship between the amount of money in a person's bank account and their age, we need to first create a linear model of the data. Assuming we have a dataset of (age, bank account) pairs, we can create a linear model using linear regression. Let the model be:
bank account = β0 + β1 * age + ε
where β0 and β1 are the intercept and slope coefficients of the model, and ε is the error term.
Once we have created the model, we can calculate the residuals for each data point by subtracting the predicted value of the bank account from the actual value:
residual = bank account - (β0 + β1 * age)
We can then plot the residuals against the age values to create the residual plot. If the model is a good fit for the data, we would expect to see a random scatter of points around the horizontal axis, with no clear patterns or trends. If there is a clear pattern in the residual plot, it suggests that the model is not a good fit for the data.
In this example, we can see that the residuals are scattered randomly around the horizontal axis, with no clear pattern or trend. This suggests that a linear model is a good fit for the data.
Note that constructing a residual plot is just one way to assess the fit of a linear model. It's always a good idea to use multiple methods to check that a model is a good fit for the data.
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If p and q vary invarsely and p is 11 when q is 28, determine q when p is equal to 4
77 is the value of Q in linear equation.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
P ∝ 1/Q
PQ = K
AT P= 11
Q = 28
11 * 28 = K
K = 308
AT P = 4
4Q = 308
Q = 77
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y is inversely proportional to the square of x. It is given that y = 8 for a particular value of x. k= When x increases by 300%, find the new value of y,
Answer:
1/2 or .5
Step-by-step explanation:
If y is inversely proportional to the square of x, we can express this relationship using the formula:
y = k/x^2
where k is a constant of proportionality. We are told that y = 8 for a particular value of x, so we can substitute these values into the equation:
8 = k/x^2
To find the value of k, we can solve for it:
k = 8x^2
Now we are asked to find the new value of y when x increases by 300%. This means that the new value of x will be 4 times the original value (since an increase of 300% means an increase by a factor of 3, and we need to add the original value to get the new value). So we can substitute 4x for x in our equation:
y = k/(4x)^2 = k/16x^2
We already know the value of k, so we can substitute it in and simplify:
y = (8x^2)/(16x^2) = 1/2
Therefore, the new value of y is 1/2 when x increases by 300%.
a certain congressional committee consists of 13 senators and 9 representatives. how many ways can a subcommittee of 5 be formed if at least 2 of the members must be representatives?
Answer:
Step-by-step explanation:
If point is slid(translated) 4 units to the right, what would the new coordinates be (3,-4)
Work out the fraction and ratio that
complete the equations below.
Give each answer in its simplest form.
a) h:k=5:6
h =
k
b) 2x=9y
x:y
=
:
The fraction and ratio that complete the equations in its simplest term is 5/6k and 2 : 9 respectively.
What is the fraction and ratio that complete the equations?h : k = 5 : 6
h/k = 5/6
cross product
h × 6 = k × 5
6h = 5k
divide both sides by 6
h = 5/6k
Then,
2x = 9y
2/9 = x/y
2 : 9 = x : y
Ultimately, the simplest form of fraction and ratio which completes the equation is 5/6k and 2:9.
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Jayden evaluated the expression a + (2 + 1. 5) for a = 14. He said that the value of the expression was 8. 5. Select all the statements that are true. Jayden's solution is incorrect. Jayden added inside the parentheses before dividing. Jayden substituted the wrong value for a. Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
It is true that Jayden's solution is incorrect. It is false that Jayden added inside the parentheses before dividing.
It is false that Jayden substituted the wrong value for a. It is true that Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
1) The correct solution is
Given,
a ÷ (2 + 1. 5)
Substituting the value of a which is 14
= 14 ÷ (2 + 1. 5)
= 14 ÷ 3.5
= 4
2) As there is no term which needs to be divided so, the second statement is false.
3) Jayden didn't substitute the wrong value of a he just solved the given expression without considering the bracket and divided the 14 which is the value of a by 2.
4) Jyaden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
i.e. a ÷ (2 + 1. 5)
14 ÷ 2 + 1. 5
7+1.5
8.5
This is the way Jayden solved the equation due to which he arrived at the wrong solution.
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The Correct question is as below
Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement.
1. Jayden's solution is incorrect.
2. Jayden added in the parentheses before dividing.
3. Jayden substituted the wrong value for a.
4. Jayden divided 14 by 2 and added 1.5
Write a method removeAll that removes all occurrences of a particular value. For example, if a variable list contains the following values:[3, 9, 4, 2, 3, 8, 17, 4, 3, 18]The call of list.removeAll(3); would remove all occurrences of the value 3 from the list, yielding the following values:[9, 4, 2, 8, 17, 4, 18]If the list is empty or the value doesn't appear in the list at all, then the list should not be changed by your method. You must preserve the original order of the elements of the list.
It should be noted that this approach follows the need to maintain the list's original order of elements.
what is function ?A function is a relationship between a set of possible outcomes (referred to as the range) and a set of inputs (referred to as the domain), with the property that each input is associated to exactly one output. A function, then, is a mathematical rule that designates a specific output value for each input value. Equations, graphs, and tables are frequently used to represent functions. They are employed to mimic real-world occurrences and to address issues in numerous branches of mathematics, science, engineering, and other disciplines.
given
The value to be deleted from the list is represented by an integer value that the method accepts as an argument.
The method iterates through the list's components using a while loop.
The method determines if the current element equals the requested value while it is in the loop. If so, the procedure uses the ArrayList class's remove method to remove the element from the list. If not, the method increases the index variable and moves on to the next element.
The procedure keeps going over the list until all instances of the given value have been eliminated.
It should be noted that this approach follows the need to maintain the list's original order of elements.
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Here is a sketch of a curve.
The equation of the curve is y = x² + ax + b
where a and b are integers.
The points (0, -7) and (7, 0) lie on the curve.
Find the coordinates of the turning point of the curve.
Finish your answer by writing, Turning point at (..., ...)
YA
O
+
[tex]{\Large \begin{array}{llll} y=x^2+ax+b \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=-7 \end{cases}\implies -7=0^2+a(0)+b\implies \boxed{-7=b} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=7\\ y=0 \end{cases}\implies 0=7^2+a7+\stackrel{b}{(-7)}\implies 0=49+7a-7 \\\\\\ 0=42+7a\implies -42=7a\implies \cfrac{-42}{7}=a\implies \boxed{-6=a} \\\\\\ ~\hfill {\Large \begin{array}{llll} y=x^2-6x-7 \end{array}}~\hfill[/tex]
now, let's get the "vertex" using the coefficients.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -6}{2(1)}~~~~ ,~~~~ -7-\cfrac{ (-6)^2}{4(1)}\right) \implies \left( - \cfrac{ -6 }{ 2 }~~,~~-7 - \cfrac{ 36 }{ 4 } \right) \\\\\\ \left( 3 ~~~~ ,~~~~ -7 -9 \right)\implies {\Large \begin{array}{llll} (3~~,~-16) \end{array}}[/tex]
Weight of a badminton racket is 0. 950 kg find the weight of 12 such rackets
The weight of 12 badminton rackets, each weighing 0.950 kg, is 11.4 kg.
The weight of an object refers to the force exerted by gravity on that object. This force is typically measured in units of mass, such as kilograms or pounds. In the case of badminton rackets, the weight is usually measured in grams.
Now, let's consider the weight of a single badminton racket. You've been given the information that the weight of one racket is 0.950 kg. This means that the force exerted by gravity on that racket is 0.950 kg.
If you want to find the weight of 12 such rackets, you need to multiply the weight of one racket by 12. This gives you:
0.950 kg x 12 = 11.4 kg
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Pls help me
Hunter is playing a video game on his tablet. The screen on the tablet is 8 inches long and 6 inches tall. The monster he is fighting on-screen is 5 inches tall. If Hunter connects his tablet to a 40-inch TV screen with the same 4:3 aspect ratio, how tall will the monster be?
The height of the monster on the 40-inch TV screen will be 8 inches, which is larger than its height on Hunter's tablet.
First, we need to find out the scale of the monster on Hunter's tablet, which can be calculated as follows
Screen aspect ratio = 8/6 = 4/3
Height of monster on tablet = 5 inches
Width of monster on tablet = (4/3) x 5 = 6.67 inches (because the aspect ratio is 4:3, the width of the monster is 4/3 times its height)
Next, we need to find out the height of the monster on the 40-inch TV screen, which has the same 4:3 aspect ratio as the tablet screen. We can do this by using a proportion
Tablet screen height, Tablet screen width = TV screen height : TV screen width
Substituting the values we know, we get,
6 inches : 8 inches = TV screen height : 10.67 inches (because 40 inches is 4/3 times the width of the TV screen)
Solving for TV screen height, we get,
TV screen height = (6/8) x 10.67 = 8 inches
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A car travelling at a constant speed travels 60 km 30 minutes .how far will it travel in 2hrs,if it continues at the same constant speed
Answer: 240 miles in 2 hours
Step-by-step explanation:
we know the car is traveling 60 km per half hour (30 minutes)
so to find km per hour, multiply both by 2.
the rate of speed is 120 miles per 60 minutes (1 hour)
multiply 120 mph by the 2 hours given = 240 miles in 2 hours
Answer:
240 km in 2 hours
Step-by-step explanation:
If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:
Speed = distance ÷ time
Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour
Since the car is traveling at a constant speed, we can use the formula:
Distance = Speed × Time
To find how far the car will travel in 2 hours, we can substitute the values we have found:
Distance = Speed × Time
Distance = 120 km/hour × 2 hours
Distance = 240 km
Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.
Can someone please help me with this?
The measure of the side MR is given as 20
How to solve for the side MRWe have to first find the value of the angle
∠TQR = 180 - (35 + 25)
= 180 - 60
= 120 degrees
180 - 120 = 60 degrees
angle TPR = 90 degrees
next we have to find ∠PTQ
= 180 - (90 + 60)
= 180 - 150
= 30 degrees
given that TMN = TQR
TNP = PTQ
So if TMN = 35 degrees since TQR = 35 degrees
PTQ = 30, so TNP = 30 degrees
The measure of QR = 4 since MN = 4
NP = pq
np = 6
Hence the measure of MR
= 4 + 6 + 6 + 4
= 20
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