A number times 7 is at least the number plus 6.6.
Write the inequality.

To find the surface area of a triangular prism, you need to find the area of the triangular bases and add them to the areas of the rectangular sides.

Surface area of the triangular prism can be found out using the following steps:

Find the area of the triangle which is A, by the following formula.

A = 1/2 × b × hA

= 1/2 × 4 × 5A

= 10m²

Find the perimeter of the base (P) which can be calculated by adding the three sides of the triangle.

P = a + b + cP = 3 + 4 + 5P = 12m

Now find the area of each rectangle which can be calculated by multiplying the adjacent sides.A = LW = 5 × 3 = 15m²

Since there are two rectangles, multiply the area by 2.2 × 15 = 30m²Add the areas of the triangle and rectangles to get the surface area of the triangular prism:

Surface area = A + 2 × LW = 10 + 30 = 40m²

Therefore, the surface area of the given triangular prism is 40m².

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Answer: x = 4

Step-by-step explanation:

Divide each term in 5x = 20 by 5 and simplify

\(\frac{5}{5} x\) = \(\frac{20}{5}\)

\(x=4\)

Answer:

x=4

Step-by-step explanation:

5x4=20

Answer:

80 lemons

Step-by-step explanation:

Let x represent the amount of lemons that were on the tree.

We can use this to set up an equation:

\(40\%x=32\)

Note that percentages can also be written as that number over 100.

\(\frac{40}{100}x=32\)

Simplify the fraction.

\(\frac{2}{5}x=32\)

Multiply both sides by 5

\(2x=160\)

Divide both sides by 2

\(x=80\)

There were 80 lemons on the tree before he picked the lemons.

Answer:

$24

Step-by-step explanation:

Cranberries needed: 1 pound

Cost of 1 pound = $4

Almonds needed: 4 pound

Cost of 1 pound = $5

4 x 5 = $20

20 + 4 = $24

Answer:

4.80

Step-by-step explanation:

Yes, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

Here,

The differential equation (1-xy)y' = y^2

And,  y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2.

What is Differential equation?

A differential equation is a mathematical equation that relates some function with its derivatives.

Now,

To show y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2, we have to find the solution of differential equation.

The differential equation is;

\((1-xy)y'=y^2\\\\\\\\\)

\((1-xy) \frac{dy}{dx} = y^2\)

\(\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }\)

It is form of  \(\frac{dx}{dy} + Px = Qy\),

Where, P is the function of y and Q is the function of x.

Hence, Integrating factor = \(e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y\)

The solution is;

\(x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c\)

\(xy = lny + c\)

Take c = 0, we get;

\(xy = lny\\\\y = e^{xy}\)

Hence, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

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To sketch the curve of the function f(x) = x(x - 4)^3, we can follow these steps: Determine the intercepts:

x-intercept: Set f(x) = 0 and solve for x:

0 = x(x - 4)^3

This gives x = 0 and x = 4 as the x-intercepts.

y-intercept: Set x = 0 and evaluate f(x):

f(0) = 0(0 - 4)^3 = 0

Analyze the behavior around critical points:

Critical point: x = 4 (from the factor (x - 4)^3)

At x = 4, the function changes direction from decreasing to increasing.

Determine the end behavior:

As x approaches positive or negative infinity, the function also approaches positive or negative infinity, respectively. This indicates no horizontal asymptotes.

Sketch the graph:

Start by plotting the intercepts and the critical point on a coordinate plane.

x-intercepts: (0, 0) and (4, 0)

y-intercept: (0, 0)

Critical point: (4, f(4))

Based on the behavior analysis and the shape of the equation, we know that the curve will pass through the x-intercepts and the y-intercept and change direction at the critical point. The curve will resemble a cubic function with a root at x = 4.

The sketch will show a downward curve from the left side, passing through the x-axis at x = 0, reaching its minimum value at x = 4, and then curving upwards towards positive infinity.

Note: It's always helpful to use additional graphing tools or software to get a more accurate representation of the curve.

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Answer:

A

Step-by-step explanation:

Answer:

23.64

Step-by-step explanation:

\(\frac{6.6+3.2}{5}\) × (2 - 5)² + 6

= \(\frac{9.8}{5}\) × (- 3)² + 6

= 1.96 × 9 + 6

= 17.64 + 6

= 23.64

The value of the (6.6 + 3.2)/5*(2-5)²+6 is 23.64

An expression is a set of terms combined using the operations +, -, x or ÷, /

Given statement:

The sum of 6.6 and 3.2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6.

Now,

(6.6 + 3.2)/5*(2-5)²+6

=9.8/5*3²+6

=1.96*9+6

=17.64+6

=23.64

Hence, the value is 23.64.

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A reflection of across line s is correct

The correct option is (b)

"Information available from the question"

The figure shows two perpendicular lines s and r, intersecting at point Pin the interior of a trapezoid.

Line r is parallel to the bases and bisects both legs of the trapezoid. Line s bisects both bases of the trapezoid.

Analysis the figure:

Since s is a line of symmetry

(x, y) = (-x, y)

r is not a line of symmetry

∴ (x, y) ≠ (x, -y)

(a) Across line r

(x, y) = (x, -y)

This is incorrect

(b)Reflection across line s

(x ,y) = (-x, y)

This is correct

(c) Rotation of 90° clockwise

(x, y) = (y ,-x)

This is incorrect

(d) Rotation of 180° clockwise

(x, y) = (-x, -y)

This is incorrect

(e) Rotation of 270° clockwise

(x, y) = (y ,-x)

This is incorrect.

Hence, A reflection of across line s is correct.

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The number of bracelets and the number of necklaces will be 10 and 5, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

A gem dealer had a proper measure of gold to make wristbands and pieces of jewelry. The amount of gold in every armband is 5 grams and the amount of gold in every accessory is 16 grams. A goldsmith utilized 130 grams.

Let 'x' be the number of Bracelets and 'y' be the number of Necklaces. Then the equation is given as,

5x + 16y = 130

The term 16y in the equation should be a multiple of 5 to get the whole value.

If the value of y is 5. Then the number of bracelets is given as,

5x + 16(5) = 130

5x + 80 = 130

5x = 50

x = 10

The number of bracelets and the number of necklaces will be 10 and 5, respectively.

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With the help of standard deviation we can conclude our answer.

acc to our question-

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The distance between A and B is √40.

We know the coordinates of the two points A and B.

We will use the distance formula to find the distance between A and B.

Distance Formula:

d = √(x2 - x1)² + (y2 - y1)²,

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Given, the coordinates of points A and B as

A = (-7, 9)B = (-5, 3)

Using the distance formula,

d = √(x2 - x1)² + (y2 - y1)²

Substituting the values of x1, x2, y1, y2,

d = √(-5 - (-7))² + (3 - 9)²

= √2² + (-6)²

= √4 + 36

= √40

Therefore, the distance between A and B is √40, which is approximately equal to 6.3 (rounded to the nearest tenth).

d = √40 ≈ 6.3

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By examining a scatterplot, you can gain valuable insights into the relationship between the two quantitative variables x and y, such as direction, strength, form, and outliers.

From examining a scatterplot of two quantitative variables x and y, you can observe the following features about the relationship between the variables:

1. Direction: You can determine whether the relationship between the variables is positive (both variables tend to increase or decrease together) or negative (one variable tends to increase while the other tends to decrease).

2. Strength: You can assess the strength of the relationship by observing how closely the data points are clustered around an imaginary line (e.g., a straight or curved line). A strong relationship has points closely clustered, while a weak relationship has points more scattered.

3. Form: You can identify the form of the relationship, such as linear (points form a straight line) or nonlinear (points form a curve).

4. Outliers: You can detect any outliers, which are data points that do not follow the general pattern of the relationship between the variables.

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Answer:

A = $ 7,449.23

A = P + I where

P (principal) = $ 5,000.00

I (interest) = $ 2,449.23

Step-by-step explanation:

Compound Interest Equation

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Compound Interest Formulas and Calculations:

Calculate Accrued Amount (Principal + Interest)

A = P(1 + r/n)^nt

Calculate Principal Amount, solve for P

P = A / (1 + r/n)^nt

Calculate rate of interest in decimal, solve for r

r = n[(A/P)(^1/nt) - 1]

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / n[ln(1 + r/n)] = [ ln(A) - ln(P) ] / n[ln(1 + r/n)]

Formulas where n = 1 (compounded once per period or unit t)

Calculate Accrued Amount (Principal + Interest)

A = P(1 + r)^t

Calculate Principal Amount, solve for P

P = A / (1 + r)^t

Calculate rate of interest in decimal, solve for r

r = (A/P)1/t - 1

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = t = ln(A/P) / ln(1 + r) = [ ln(A) - ln(P) ] / ln(1 + r)

Continuous Compounding Formulas (n → ∞)

Calculate Accrued Amount (Principal + Interest)

A = Pe^rt

Calculate Principal Amount, solve for P

P = A / ert

Calculate rate of interest in decimal, solve for r

r = ln(A/P) / t

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / r

The wavelength of the wave is approximately 2.09m, and the speed of the wave is approximately 1.99m/s. values were obtained by analyzing given expression and utilizing relationships between wave parameters.

To find the wavelength, we can use the formula λ = v/f, where λ represents the wavelength, v represents the speed of the wave, and f represents the frequency of the wave. However, in the given expression, we are not directly given the frequency. Instead, we have the angular frequency ω, which is related to the frequency as ω = 2πf.By comparing the given expression with the general wave equation, we can identify that the wave number k = 3.00m^(-1). Since the wave number is related to the wavelength as k = 2π/λ, we can rearrange the equation to find the wavelength: λ = 2π/k. Plugging in value for k, we get λ = 2π/(3.00m^(-1)), which simplifies to approximately λ = 2.09m.

To determine the speed of the wave, we can use the formula v = λf, where v represents the speed of the wave, λ represents the wavelength, and f represents the frequency. As mentioned earlier, we have the angular frequency ω instead of the frequency f. However, we know that ω = 2πf, so we can rearrange this equation to find f = ω/(2π). Plugging in the given angular frequency ω = 6.00s^(-1), we get f = 6.00s^(-1)/(2π), which simplifies to approximately f = 0.955Hz.Now that we have the wavelength λ = 2.09m and the frequency f = 0.955Hz, we can use the formula v = λf to find the speed of the wave. Plugging in the values, we get v = (2.09m)(0.955Hz), which gives us the speed of the wave v = 1.99m/s.

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Answer:

see explanation

Step-by-step explanation:

(i)

to find h(g(x)) , substitute x = g(x) into h(x) , that is

h(g(x))

= h(2x - 3)

= 4(2x - 3)

= 8x - 12

(ii)

given

h(g(x)) = \(\frac{1}{2}\) g(x) , then

8x - 12 = \(\frac{1}{2}\) (2x - 3) ← multiply both sides by 2 to clear the fraction

16x - 24 = 2x - 3 ( subtract 2x from both sides )

14x - 24 = - 3 ( add 24 to both sides )

14x = 21 ( divide both sides by 14 )

x = \(\frac{21}{14}\) = \(\frac{3}{2}\) = 1.5

Answer:

1.

7/8 of a ounce is 0.875 oz

0.875 divided by 8.5 is 9.7

9.7 is the serving in the whole bag

9.7 times the amount of calories

it would be 1746 cals

Step-by-step explanation:

Answer:172.72

Step-by-step explanation:

68 inches = 172.72 centimeter

How to convert inches to centimeter ?

Add 2.54 centimeters to the provided inch value to convert it to centimeters. For instance, multiply 7 by 2.54 to translate from inches to centimeters.

What is centimeter ?

The International System of Units' centimeter (SI symbol cm), sometimes known as a centimeter (international spelling) or centimeter (American spelling), is a unit of length (SI),

Exactly how big is one inch?

A yard and a foot are equivalent to an inch. A metric inch is precisely 2.54 centimeters. One whole inch is made up of two half inches and four quarter inches.

what is a inch ?

The British imperial and American customary systems of measurement both use the inch as their standard unit of length (symbolised as in or ′′). It is the same as 1/36 of a yard 

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The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Answer:

the second one

Step-by-step explanation:

Answer: im on the same question

Step-by-step explanation:

sorry

The probability is the ratio of the favorable event to the total number of events. Then the probability of the elk caught in the park being unmarked will be 92.44%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.

The total number of elk is 5,625.

The number of elk that were marked is 225.

Then the number of elk that were unmarked will be

→ 5625 - 225 = 5,200

Then the probability of the elk caught in the park being unmarked will be

\(\rm P = \dfrac{5200}{5625}\\\\P = 0.9244 \ or \ 92.44\%\)

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Answer:

1/6

Step-by-step explanation:

There are 6 large squares here, all of which have been shaded but for one.

Thus, the desired fraction is 1/6.

Answer:

No

Step-by-step explanation:

4/9 divided by 5/7 is equal to 4/9 * 7/5 = 28/45. We can see that 63/20 is not equivalent to 28/45 as 28/45 is less than one and 63/20 is greater than one.

Answer:

It's Store C

Hope this helps :)

Step-by-step explanation:

Got it right on USA TEST PREP :)

Answer:

The correct option is;

B) Discrete linear

Step-by-step explanation:

The graph shows scatter plots of the data points and therefore the plot is a discrete plot of points. Also, we have, from the graph of the function, changes in input values are proportional with changes in output, such that the progression of the points are unidirectional.

Therefore, the graph is a discrete linear function.

Answer:

ST ≈ 10.9 ft

Step-by-step explanation:

Using the sine ratio in the right triangle

sin32° = \(\frac{opposite}{hypotenuse}\) = \(\frac{US}{ST}\) = \(\frac{5.8}{ST}\) ( multiply both sides by ST )

ST × sin32° = 5.8 ( divide both sides by sin32° )

ST = \(\frac{5.8}{sin32}\) ≈ 10.9 ( to the nearest tenth )

Answer:

its b

Step-by-step explanation:

Time interval 6:53 a.m to 8:53 a.m, the average rate of change per hour the greatest.

Given,  

Time          Temperature (°F)  

5:53 a.m.       60.1

6:53 a.m.       60.1

8:53 a.m.       66.9

11:53 a.m        75.2

3:53 p.m.        78.1

From 5:53 a.m. to 6:53 a.m. the temperature is constant. So average rate of change per hour is 0.

From 6:53 a.m to 8:53 a.m. the temperature is increasing from 60.1 to 66.9 or 6.8 in 2 hours . So average rate of change per hour is \(\frac{6.8}{2} =3.4\).

From 8:53 a.m. to 11:53 a.m the temperature is again increasing from 66.9 to 75.2 or 8.3 in 3 hours. So average rate of change per hour is \(\frac{8.3}{3} =2.76\).

From 11:53 a.m to 3:53 p.m. the temperature is again increasing from 75.2 to 78.1 or 2.9 in 4 hours. So average rate of change per hour is \(\frac{2.9}{4}=0.725\).

Now clearly from the above points time interval 6:53 a.m to 8:53 a.m, the average rate of change per hour the greatest.

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Answer: 25

Step-by-step explanation: