At the local Convenience store William and Sarah are getting snacks for the friends. William buys 3 soft drinks and 2 hot dogs at a cost of $7.70, while Sarah buys 2 soft drinks and 1 hot dog at cost of $ 4.55.
Find the cost of 1 soft drink and 1 hot dog.

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

When the temperature (T) is 10 K, the value of T^4 is 10,000. This indicates that T raised to the power of 4 is equal to 10,000. Among the provided answer choices, the correct one is "10,000".  

It's important to note that raising a number to the fourth power means multiplying the number by itself four times, resulting in a significant increase in value compared to the original number.

To find the value of T^4 when T is 10 K, we need to raise 10 to the power of 4. This means multiplying 10 by itself four times: 10 × 10 × 10 × 10. Performing the calculations, we get:

T^4 = 10 × 10 × 10 × 10 = 10,000

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Answer:

99010

Step-by-step explanation:

Answer:

123.1323

Step-by-step explanation:

By the definition of similar polygons, the lengths of corresponding sides are proportional.

The proportion for \(x=40\).

As it is given in the definition, similar polygons have congruent angles and proportional sides.

Therefore, by the definition of similar polygons, the lengths of corresponding sides are proportional.

Cross multiply and solve the proportion  \(x\) as follows:

The blank should be proportional.

\(\frac{12}{8} =\frac{20+x}{x}\\ 12x=160+8x\\4x=160\\x=40\)

Therefore, the proportion for \(x=40\).

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The approximate population variance is 937.85.

To approximate the population variance, we need to calculate the sample variance first and then use the following formula to approximate the population variance:

Population variance ≈ (sample variance) × [(n)/(n-1)], where n is the sample size.

To calculate the sample variance, we need to first calculate the sample mean:

Sample mean = (Σ (midpoint of class interval × frequency))/n

= [(9.5 × 15) + (29.5 × 13) + (49.5 × 8) + (69.5 × 10) + (84.5 × 10)]/56

= 44.375

Next, we can use the formula for calculating the sample variance:

Sample variance = [(Σ(frequency × (midpoint of class interval - sample mean)^2))/(n-1)]

= [(15 × (9.5-44.375)^2) + (13 × (29.5-44.375)^2) + (8 × (49.5-44.375)^2) + (10 × (69.5-44.375)^2) + (10 × (84.5-44.375)^2)]/55

= 918.75

Finally, we can use the formula to approximate the population variance:

Population variance ≈ (sample variance) × [(n)/(n-1)]

= 918.75 × [(56)/(55)]

≈ 937.85

Therefore, the approximate population variance is 937.85.

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Answer :

an = 15 + (9-1) 14

an = 15 + (8) 14

an = 15 + 112

an = 127 is the answer

Hope it helped

Answer:

Only the second one is true:

It has a constant rate of change.

Step-by-step explanation:

Answer:

In the 6% account, 13,000 was deposited

In the 10% account, 20,000 was deposited

Step-by-step explanation:

Here, we are interested in calculating how much invested in each account

.

Let the amount invested be $x and $y

Mathematically;

x + y = 33,000 ••••(i)

Now let’s work with interest

6% of x + 10% of y = 2780

6/100 * x + 10/100 * y = 2780

Multiply through by 100

6x + 10y = 278000 •••••••••(ii)

From i, x = 33,000 -y

Put this into ii

6(33,000 -y) + 10y = 278000

198,000-6y + 10y = 278000

4y = 80000

y = 80,000/4 = 20,000

But x = 33,000 -y = 33,000 -20,000 = 13,000

The value of T is 428°C.

To solve the problem, we can start by substituting the given value of R = 13946 into the equation R = 10000 + (4124 x 10^-2)T – (1779 x 10^-5)T^2 and solving for T. This gives us a quadratic equation in T which can be solved using the quadratic formula.

After simplifying, we get T = 427.67°C or T = -88.22°C. However, we know that the thermometer is only used if T ≤ 600°C, so the only valid solution is T = 427.67°C.Therefore, the temperature corresponding to a resistance of 13946 ohms is approximately 428°C.

It's important to note that this assumes the thermometer is operating within its specified range and that the resistance-temperature relationship remains linear over the given temperature range.

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Answer:

 a) cannot tell

  b) congruent

  c) not congruent

Step-by-step explanation:

You want to know if the triangles in the given figures are congruent.

In order to prove congruence, we must have information to establish one of SSS, SAS, ASA, AAS congruence.

Congruence only of corresponding angles demonstrates the triangles are similar, which means they may or may not be congruent.

These triangles have congruent corresponding angles, so are similar. It is impossible to tell if they are congruent.

These triangles meet the conditions for demonstrating AAS congruence. The triangles are congruent.

Looking at the figure from an AAS or ASA or SAS point of view, the corresponding sides are not congruent, but the corresponding angles are. These triangles are similar, but are not congruent.

__

Additional comment

In the triangles of (c), for the given long side, the short side shown will be 25.73 in the larger triangle and 16.73 in the smaller one. That is, the angles indicate the triangles should be similar, but the given side ratios are not proportional.

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Answer:  x = 1 or x = -4 or x = -1/2

Explanation:

The answer is y = 2x3 + 4x2 – x + 5 and  y = –3x2 + 4x + 9

Roots are both: x=-4, x= -1/2 , x= 1

Proof:

Solve for x over the real numbers:

2 x^3 + 4 x^2 - x + 5 = -3 x^2 + 4 x + 9

Subtract -3 x^2 + 4 x + 9 from both sides:

2 x^3 + 7 x^2 - 5 x - 4 = 0

The left hand side factors into a product with three terms:

(x - 1) (x + 4) (2 x + 1) = 0

Split into three equations:

x - 1 = 0 or x + 4 = 0 or 2 x + 1 = 0

Add 1 to both sides:

x = 1 or x + 4 = 0 or 2 x + 1 = 0

Subtract 4 from both sides:

x = 1 or x = -4 or 2 x + 1 = 0

Subtract 1 from both sides:

x = 1 or x = -4 or 2 x = -1

Divide both sides by 2:

Answer:  x = 1 or x = -4 or x = -1/2

The letters can be added together if they have similar variables.

B and C are like terms. Option B shows the like terms of letters.

A mathematical expression consisting of two terms connected by a plus sign or minus sign is called the binomial expression.

The attachment shows the table of letters and variables.

To multiply binomials, a form of the distributive property is used.

The table has been complete with the final values of letters which are given below.

\(A= (-2x) \times 4x\)

\(A = -8x^2\)

\(B = 3 \times 4x\)

\(B = 12 x\)

\(C = (-2x)\times 1\)

\(C = -2x\)

\(D = 3\times 1\)

\(D = 3\)

From the final values of letters, B and C are the only like terms, they can be added together since they have similar variables.

Hence we can conclude that B and C are like terms. Option B shows the like terms of letters.

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Answer:B

Step-by-step explanation:

took the test

The change in one variable related to the change in more than one other variable is measured using multiple regression analysis.

A statistical method known as multiple regression is used on datasets intended to show a link between a single response or dependent variable and a number of independent factors.

Even though linear regression is frequently employed, it can only be utilized with one independent variable and one dependent variable. Non-linear regression is not predicted by linear regression, which is also limited to the training dataset.

We employ multiple regression to account for the same restrictions. It focuses on removing one particular limitation, which is allowing for the analysis of multiple independent variables.

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Answer:

Use the information given to write an equation in standard form.  

Slope is -3, and (0, -4) is on the line.  

Step-by-step explanation:

Answer:

24.99

Step-by-step explanation:

25.9-6.91=24.99

The series diverges according to the Root Test.

To test the convergence of the series using the Root Test, we need to evaluate the limit of the absolute value of the nth term raised to the power of 1/n as n approaches infinity. In this case, our series is:

∑(n=1 to ∞) ((2n + 6)/(3n + 1))^n

Let's simplify the limit:

lim(n → ∞) |((2n + 6)/(3n + 1))^n| = lim(n → ∞) ((2n + 6)/(3n + 1))^n

To simplify further, we can take the natural logarithm of both sides:

ln [lim(n → ∞) ((2n + 6)/(3n + 1))^n] = ln [lim(n → ∞) ((2n + 6)/(3n + 1))^n]

Using the properties of logarithms, we can bring the exponent down:

lim(n → ∞) n ln ((2n + 6)/(3n + 1))

Next, we can divide both the numerator and denominator of the logarithm by n:

lim(n → ∞) ln ((2 + 6/n)/(3 + 1/n))

As n approaches infinity, the terms 6/n and 1/n approach zero. Therefore, we have:

lim(n → ∞) ln (2/3)

The natural logarithm of 2/3 is a negative value.Thus, we have:ln (2/3) <0.

Since the limit is a negative value, the series diverges according to the Root Test.

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The probable question may be:
Test the series below for convergence using the Root Test.

sum n = 1 to ∞ ((2n + 6)/(3n + 1)) ^ n

The limit of the root test simplifies to lim n → ∞  |f(n)| where

f(n) =

The limit is:

(enter oo for infinity if needed)

Based on this, the series

Diverges

Converges

The function \(f(x) = 3x^4 - 30x^3 + x - 3\) is concave upward in the intervals (-∞, 0) and (5, +∞), and concave downward in the interval (0, 5).

To determine where the function \(f(x) = 3x^4 - 30x^3 + x - 3\) is concave upward or concave downward, we need to analyze the second derivative of the function.

First, let's find the first derivative of f(x) with respect to x:

\(f'(x) = 12x^3 - 90x^2 + 1\)

Next, let's find the second derivative by taking the derivative of f'(x):

\(f''(x) = 36x^2 - 180x\)

Now, we can determine where the function is concave upward and concave downward by analyzing the sign of the second derivative.

To find the critical points, we set f''(x) = 0 and solve for x:

\(36x^2 - 180x = 0\)

36x(x - 5) = 0

This equation gives us two critical points: x = 0 and x = 5.

Next, we evaluate the sign of the second derivative f''(x) in the intervals separated by the critical points:

For x < 0:

We can choose x = -1 for evaluation. Substituting into f''(x):

\(f''(-1) = 36(-1)^2 - 180(-1)\)

= 36 + 180

= 216 (positive)

Since f''(x) > 0, the function is concave upward in this interval.

For 0 < x < 5:

We can choose x = 1 for evaluation. Substituting into f''(x):

\(f''(1) = 36(1)^2 - 180(1)\)

= 36 - 180

= -144 (negative)

Since f''(x) < 0, the function is concave downward in this interval.

For x > 5:

We can choose x = 6 for evaluation. Substituting into f''(x):

\(f''(6) = 36(6)^2 - 180(6)\)

= 1296 - 1080

= 216 (positive)

Since f''(x) > 0, the function is concave upward in this interval.

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The probability density function (pdf) of the largest of the five waiting times is given by: f(x) = 4/10^5 * x^4, where x is a real number between 0 and 10. The expected value of the largest of the five waiting times is 8.33 minutes.

The pdf of the largest of the five waiting times can be found by considering the order statistics of the waiting times. The order statistics are the values of the waiting times sorted from smallest to largest.

In this case, the order statistics are X1, X2, X3, X4, and X5. The largest of the five waiting times is X5.

The pdf of X5 can be found by considering the cumulative distribution function (cdf) of X5. The cdf of X5 is given by: F(x) = (x/10)^5

where x is a real number between 0 and 10. The pdf of X5 can be found by differentiating the cdf of X5. This gives: f(x) = 4/10^5 * x^4

The expected value of X5 can be found by integrating the pdf of X5 from 0 to 10. This gives: E[X5] = ∫_0^10 4/10^5 * x^4 dx = 8.33

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Answer:

the too left graph us the abswer,

Because

f(x) = (x + 3)(x - 2) has positive cieff of the x^2 term, and also it has roots of -3 and 2

The graph of the function  f(x) = (x + 3)(x - 2) is first graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

To graph the function f(x) = (x + 3)(x - 2), we can start by finding its x-intercepts, y-intercept, and any vertical or horizontal asymptotes.

First, to find the x-intercepts, we set y = 0 and solve for x:

(x + 3)(x - 2) = 0

This equation is true when x = -3 or x = 2. Therefore, the x-intercepts of the graph are -3 and 2.

Next, to find the y-intercept, we set x = 0 and evaluate:

f(0) = (0 + 3)(0 - 2) = -6

Therefore, the y-intercept of the graph is -6.

The graph of f(x) = (x + 3)(x - 2) is a parabola that opens up because the sign of the two factors, (x + 3) and (x - 2), are both positive.

This means that the graph of f(x) will be a parabola that opens up with its vertex located at the point where the two factors are equal to each other

Hence, the graph of the function  f(x) = (x + 3)(x - 2) is first graph.

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Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

cos A = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AB}{AC}\) = \(\frac{18}{30}\) = \(\frac{3}{5}\)

Answer:

£34

Step-by-step explanation:

15/100*£40

=£6

£40_£6

=£34

Answer:  c. \(\frac{1}{a}\).

Step-by-step explanation:

10 = 2 - 4(ax - 3)

10 = 2 - 4ax + 12

10 = 14 - 4ax

Minus 14 on both sides.

-4 = -4ax

Divided -4 on both sides.

1 = ax

Divided a by both sides to solve x.

\(\frac{1}{a}\) = x

Therefore, the answer is c.

Answer:

The volume is 83.6 cubic inches.

Step-by-step explanation:

We know that the battery is cylindrical, so we can use the formula:

\(\pi r^{2} h\)

We can use 3.14 for \(\pi\), and we know that the radius is 2.2 with a height of 5.5.

Let's set up the equation:

3.14 · 2.2² · 5.5= volume

=83.5868, which rounded to the nearest tenth would equal 83.6.

Hope this helps! :)

We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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The rate of change of z with respect to t, dz/dt, at (x,y) = (4,0) is equal to 48, based on the given equations and the differentiation of z³ = x³ + y².

To find dz/dt at (x,y) = (4,0), we need to differentiate the equation z³ = x³ + y² with respect to t.

Differentiating both sides of the equation, we get:

3z² * dz/dt = 3x² * dx/dt + 2y * dy/dt

Given dx/dt = 3 and dy/dt = 2, and since (x,y) = (4,0), we have

3z² * dz/dt = 3(4)² * 3 + 2(0) * 2

3z² * dz/dt = 3(16) * 3

3z² * dz/dt = 144z²

Now, let's solve for dz/dt

dz/dt = (144z²) / (3z²)

dz/dt = 48

Therefore, dz/dt at (x,y) = (4,0) is equal to 48.

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