Three cards are chosen at random from a deck of 52 playing cards. What is the probability that they
(a) are all aces.
(b) all have the same value.
(c) two of them have the same value
(d) all have different values.

3 is to 2 is the probability of drawing 4 marbles that are all blue.

Answer:

44.4°

Step-by-step explanation:

Two complementary angles add up to 90°. Let's call one of the two x, and the second 90-x (in fact, \(x+(90-x) = 90\)).

At this point we can use the second condition: the first angle, plus 1.2°, is equal to the complementary.

\(x+1.2=90-x \rightarrow 2x=88.8 \rightarrow x = 44.4\)

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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The interest rate is 10.89%

1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..

The size of the nominal money supply in the new short-run equilibrium is 121.07.

2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.

Real exchange rate will remain unchanged.

3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.

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\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{37}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{35} \end{cases} \\\\\\ x=\sqrt{ 37^2 - 35^2}\implies x=\sqrt{ 1369 - 1225 } \implies x=\sqrt{ 144 }\implies x=12\)

Answer:

1) x=1/2-y/2-3z

2)x= 16/3- 2y/3- 5z/3

3)x= 11/7- 3y/7+ 4z/7

Step-by-step explanation:

isolate the variable, to do that divide each side by the factors that don't contain the variable

Answer: She jump ropes 7/3 or 2 1/3 of an hour every week

Step-by-step explanation: This is because she jump ropes 1/3 each day and there's 7 days in a week so 7/3 or 2 1/3(2 hours and 20 minutes)

I hope you are having a nice day!

Answer:

2 hours 33 minutes

Step-by-step explanation:

1/3 of an hour is 20 minutes

20 times 7 is 140

140 divided by 60 is 2.33 hours

so 2 hours and 33 minutes

\(\sqrt{((-6)-(-5))^2 +(9-2)^2}=5\sqrt{2} \approx 7.071\)

Answer:

The factored form is,

\((4a^2+2a+1)(4a^2-2a-1)\)

Step-by-step explanation:

We have,

\(16a^4-4a^2-4a-1\\factoring,\\We\ can \ write \ 16a^4 \ as \ (4a^2)^2\\Also,\\then we have,\\(4a^2)^2-(4a^2+4a+1)\\Now, 4a^2 + 4a + 1 \ is \ a \ perfect \ square,\\4a^2 + 4a + 1 = (2a)^2 + 2(2a) + 1\\= (2a + 1)^2\\so, we \ have,\\(4a^2)^2 - (2a + 1)^2\\\)

Using the difference of square formula,

\(x^2 - y^2 = (x+y)(x-y)\\with,\\x = 4a^2,\\y = 2a+1,\\we \ get,\\(4a^2+2a+1)(4a^2-2a-1)\)

Which is the factored form,

Answer:

-----------------------

Let Anita be x now.

Her mother is 5 times older and in two years time she will be 5x + 2.

Rita is half the age of Anita and in two years time she will be (x/2) + 2.

The sum of ages after two years will be 58:

Anita is 8 years old.

Answer:

a=18.1 or √329

Step-by-step explanation:

a²+b²=c²

a²+20²=27²

a²+400=729

a²=329

a=18.1 or √329 depending on what form you are answering in, radical or decimal.

The Hillsdale is 8 km from the Kinsley's house

Let Kinsley's house be A

     Summerfield be B

     Hillsdale be C

The Kinsley's house due west of Summerfield be AB which is 6 km and The distance between Summerfield and Hillsdale is BC which is 10 km

Distance between Kinsley's house and Hillsdale can be calculated using Pythagoras' theorem, which states that the square of the hypotenuse is equal to the sum of the square of the other two sides.

        BC² = AB² + AC²

 We need AC, so let us rewrite this equation

        AC² = BC² - AB²

        AC²  =  10² - 6²

        AC² = 100 - 36

        AC² = 64

        AC = √64

        AC = 8 km

Therefore, Kinsley's house is due south of Hillsdale from 8 km

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Using the binomial distribution, it is found that there is a 0.9815 = 98.15% probability that at least one of them has been vaccinated.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem, the values of the parameters are:

n = 5, p = 0.55

The probability that at least one of them has been vaccinated is given by:

\(P(X \leq 1) = 1 - P(X = 0)\)

In which:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{5,0}.(0.55)^{0}.(0,45)^{5} = 0.0185\)

Then:

\(P(X \leq 1) = 1 - P(X = 0) = 1 - 0.0185 = 0.9815\)

0.9815 = 98.15% probability that at least one of them has been vaccinated.

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Answer:

common difference is 0.5

first term is 5

Step-by-step explanation:

use the formula for the nth term of an ap Tn=a+(n-1)d

T12=10.5

T18=13.5

therefore come up with two equations

T12=a+(12-1)d

10.5=a+11d(1st equation)

T18=a+(18-1)d

13.5=a+17d(2nd equation)

then solve both as a simultaneous equation

a+11d=10.5

a+17d=13.5

-6d/-6=-3/-6

d=0.5

use one of the equations to find the first term

a+11(0.5)=10.5

a+5.5=10.5

a=10.5-5.5

a=5

I hope this helps

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Answer:

14s+107

Step-by-step explanation:

(2s+7)+(12s+100)

14s+107

The graph of g(x) is the graph of f(x) stretched vertically and reflected over the axis.

The correct option is C.

We can compare the graphs of two functions f(x)=x² and g(x)=-2/3 x² by determining their vertices, domain, range, axis of symmetry, and shape of the graphs. The vertex of f(x)=x² is at the origin (0,0), which means that the parabola opens upward and is symmetrical around the y-axis.

The domain is all real numbers, and the range is y≥0. The axis of symmetry is the y-axis. On the other hand, the vertex of g(x)=-2/3 x² is also at the origin, and it opens downward. It is also symmetrical around the y-axis. The domain is all real numbers, and the range is y≤0.

The axis of symmetry is the y-axis, just like f(x).It is important to remember that g(x) is the negative of f(x), which indicates that g(x) is reflected across the x-axis. Furthermore, the stretch factor is 2/3, which makes the graph of g(x) flatter than the graph of f(x) and it is  stretched vertically and reflects over x axis(option c).

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Answer:

a = 1000, p = 10

Step-by-step explanation:

Given

y = - 3lg x + lg a

in the form y = mx + c ( m is the slope and c the y- intercept )

From the graph

(a)

c = 3 , then

lg a = 3 , that is

a = 10³ = 1000

(b)

Replace x by p and y = 0 in the equation

0 = - 3lg p + 3 ( subtract 3 from both sides )

- 3 = - 3lg p ( divide both sides by - 3 )

1 = lg p

p = 10 [ \(log_{10}\) 10 = 1 ]

=======================================

Work Shown:

1 liter = 1000 mL

3 liters = 3000 mL

I multiplied both sides by 3.

Divide that result over 500 to get 3000/500 = 6

So she'll need to buy 6 cartons.

-------

You could also solve like this:

(1 carton)/(500 mL) = (x cartons)/(3000 mL)

1/500 = x/3000

1*3000 = 500*x ... cross multiply

3000 = 500x

500x = 3000

x = 3000/500 .... dividing both sides by 500

x = 6

The estimated sales for a shopping center with a total square footage of 5.3 billion is approximately $1016.58 billion.

Let's calculate the estimated sales for a shopping center with a total square footage of 5.3 billion.

Using the regression line equation y = 596.014x - 2143.890, we substitute x = 5.3 billion into the equation to find the estimated sales:

y = 596.014 * 5.3 - 2143.890

y ≈ 3160.4742 - 2143.890

y ≈ 1016.5842

First, we calculate the total sum of squares (SST) by summing the squared differences between the actual sales (y) and their average value:

SST = (855.8 - 919.76)² + (940.8 - 919.76)² + (979.7 - 919.76)² + (1058.6 - 919.76)² + (1123.3 - 919.76)² + (1207.1 - 919.76)² + (1278.4 - 919.76)² + (1341.7 - 919.76)² + (1446.9 - 919.76)² + (1526.8 - 919.76)²

Next, we calculate the sum of squares of residuals (SSR) by summing the squared differences between the actual sales (y) and the sales predicted by the regression line equation:

SSR = (855.8 - (596.014 * 5.1 - 2143.890))² + (940.8 - (596.014 * 5.2 - 2143.890))² + ... + (1526.8 - (596.014 * 6.1 - 2143.890))²

Finally, we substitute the values of SSR and SST into the R² formula:

R² = 1 - (SSR / SST)

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Answer:

Step-by-step explanation:

6s³ + 9s + 10 + 3s³ + 4s - 10

Collect like terms

6s³ + 3s³ + 9s + 4s + 10 - 10

Since, two opposites add up to zero, remove them from the expression

6s³ + 3s³ + 9s + 4s

add the like terms

9s³ + 13s

hope this helps..

best regards!!

Answer:

9s^3+13s

Step-by-step explanation:

Add each term:

9s^3+13s

I hope this helps...

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Answer:

the answer is 0.3%

Step-by-step explanation:

12 divided by 40 is 0.3

Answer:

30%

Step-by-step explanation:

Write a proportion.

12 / 40 = x / 100

Cross multiply.

40x = 1200

Solve for x.

x = 30

She ate 30% of the chips.

Answer:

The answer is A

Step-by-step explanation:

Camie: $5x + $50 = $55 ( for now/i think)

Jorge: $7x

The  equation to represent  Jorge has saved at least the same amount as Camie is 7w = 5W + 50.

The correct option is (A)

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Given:

Camie saves $5 per week plus $50 she receives for her birthday.

Jorge saves $7 per week.

Now, Jorge have to achieve the same amount as Camie.

let w be the number of weeks.

Then equation can be represented as

7w = 5W + 50

Here 7w is amount by Jorge and 5W + 50 is amount of Camie.

Hence, the equation to represent  Jorge has saved at least the same amount as Camie is 7w = 5W + 50.

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Answer: 1 is 50 and 2 is 70

Step-by-step explanation: these are both congruent and they are supplementary triangles

Because the triangles are just translated meaning they are moved and they are supplementary meaning they add up to 180° so we can subtract 180-70-60 to get 50 and the equation of triangle XYZ is 180-60-50 to get 70 those are the answers hope this helps :)

The expected number of left-handed students in a typical class of 188 students can be estimated using the prevalence rate of left-handedness in the general population.

According to studies, approximately 10% of the population is left-handed. Therefore, we can expect around 18.8 left-handed students in a class of 188 students.

To calculate the standard deviation, we need additional information. The standard deviation depends on the variability of left-handedness in the population. Without this data, it is not possible to provide an accurate estimation of the standard deviation.

Similarly, the expected number of right-handed students can be estimated by subtracting the expected number of left-handed students (18.8) from the total number of students (188). This gives us an expected number of around 169.2 right-handed students.

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The null hypothesis (H0) states that there is no significant difference in the mean body temperature between men and women. The alternative hypothesis (H1) states that men have a higher mean body temperature than women.

Step 1: Null and Alternative Hypotheses

The null hypothesis (H0): μ1 ≤ μ2 (There is no significant difference in the mean body temperature between men and women)

The alternative hypothesis (H1): μ1 > μ2 (Men have a higher mean body temperature than women)

Step 2: Test Statistic

The test statistic for comparing the means of two independent samples with unequal variances is the t-statistic. The formula for calculating the t-statistic is:

t = (x1 - x2) / √(s1² / n1 + s2² / n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Step 3: P-Value

Using the given data:

x1 = 97.72, x2 = 97.34, s1 = 0.83, s2 = 0.63, n1 = 11, n2 = 59

Plugging these values into the t-statistic formula, we get:

t = (97.72 - 97.34) / √(0.83² / 11 + 0.63² / 59)

t = 0.38 / √(0.062 + 0.0066)

t = 0.38 / √(0.0686)

Step 4: Conclusion

At a significance level of 0.05, we compare the calculated t-statistic to the critical value from the t-distribution with (n1 + n2 - 2) degrees of freedom. If the calculated t-statistic is greater than the critical value, we reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 5: Confidence Interval

A confidence interval can be constructed to estimate the difference between the two population means. Using the given data and assuming a 95% confidence level, the confidence interval can be calculated using the formula:

CI = (x1 - x2) ± tα/2 × √(s1² / n1 + s2² / n²)

where CI is the confidence interval, tα/2 is the critical value from the t-distribution corresponding to a 95% confidence level, and all other variables are as defined above.

Therefore, the are:

The null hypothesis states that there is no significant difference in the mean body temperature between men and women, while the alternative hypothesis states that men have a higher mean body temperature than women.

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Answer:

Step-by-step explanation:

Search up the area of both. rectangle is LxW therefore the area is 18.  the other is trapezium therefore, ((a+b)xh)/2 therefore the area is 20. trapezium has larger area

Answer trapezoid has  greater area

Step-by-step explanation: rec: 6*3= 8,  trapezoid [ (6+2) * 5 ]1/2  = 20

To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

where:

Q is the discharge (flow rate)

n is Manning's coefficient (0.014 in this case)

A is the cross-sectional area of the channel

R is the hydraulic radius of the channel

S is the slope of the channel bed

First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:

A = π * r^2 = π * (3m)^2 = 9π m^2

Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:

R = r = 3m

Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:

S = 1/600

Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):

Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)

Using a calculator, the discharge can be evaluated to get the final result.

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At the crucial integers where the second derivative of (x) changes sign, local extrema happen. It is a local minimum if the second derivative crosses a key threshold from negative to positive.

Let's denote the total cost function as C(x), where x is the number of vests produced in one day. The average cost per vest is given by Ĉ(x) = C(x) / x.

The critical numbers of Ĉ(x), we need to calculate its first derivative with respect to x and set it equal to 0. The critical numbers will be the values of x that satisfy this equation.

The intervals where the average cost per vest is decreasing or increasing can be determined by analyzing the sign of the first derivative of Ĉ(x). If the first derivative is negative, the average cost is decreasing, and if it is positive, the average cost is increasing.

Finally, local extrema occur at the critical numbers where the second derivative of Ĉ(x) changes sign. If the second derivative changes from negative to positive at a critical number, then it is a local minimum. If it changes from positive to negative, it is a local maximum.

To summarize, you will need to:

1. Write the average cost function Ĉ(x) = C(x) / x
2. Calculate the first and second derivatives of Ĉ(x)
3. Find the critical numbers by setting the first derivative equal to 0
4. Determine the intervals where the average cost is increasing or decreasing by analyzing the sign of the first derivative
5. Identify local extrema by examining the sign change of the second derivative at the critical numbers.

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Answer:

6

Step-by-step explanation:

It would only be 7 if it was 6.5 or higher so if it's 6.4 or less it'll always go back one so 6.

Whole number: Exact nuumber with no decimals such as: 1,2,3,4,5...

Answer:

6

Step-by-step explanation:

1, 2, 3, 4, slide to the floor,

5, 6, 7, 8, 9, climb the vine.