7 A basket has 40 fruits. 10 of them are apples, 25 are oranges and the rest are mangoes
By what % is the number of mangoes smaller than the number of oranges?​

Answer:

  82 mm²

Step-by-step explanation:

You want to know the surface area of a rectangular prism with dimensions 1 mm, 5 mm, and 6 mm.

The surface area can be found using the formula ...

  A = 2(LW +H(L +W))

  A = 2(5·6 + 1(5 +6)) = 2(30 +11) = 82 . . . . . square mm

The surface area is 82 square millimeters.

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Answer:

$133.56

Step-by-step explanation:

Multiply 180 and .3 and then subtract that number with 180

you should then get 126

multiply 126 by .06 you should get 7.56

Finally add 126 and 7.56 you should get your final price of 133.56

The nature of the roots of the given equation x^2 - 3x - 4 = 0 is real and unequal.

The general form of a quadratic equation is ax^2 + bx +c = 0.

Comparing the given equation x^2 - 3x - 4 = 0 with the general form of quadratic equations, we get that:

a = 1,  b = -3 and c = -4

If b^2 - 4ac > 0, then we say that the nature of the roots of the equation is real and unequal.

Therefore,  b^2 - 4ac = (-3) ^ 2 - 4 x 1 x (-4) = 25 >0

Hence, we conclude that the nature of the roots of the given equation is real and unequal.

The question is incomplete, the complete question is:

What is the nature of the roots of x² − 3x - 4 = 0?

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There is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

So, we know that:

27 black socks.

18 grey socks.

9 navy socks.

Probability formula: P(E) = Favouravle events/Total events

Now, insert values in the formula as follows:

P(E) = Favouravle events/Total events

P(E) = 27+18/27+18+9

P(E) = 45/54

P(E) = 15/18

P(E) = 5/6

Therefore, there is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.

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Correct question:
in a pitch-black room, you have a drawer with 27 black socks, 18 grey socks, and 9 navy socks. What is the probability that you take out pairs of socks to ensure you get a pair that is not navy?

The system identification of h(n) is to be found with the given x(n) and y(n). Let us solve it as follows:Given,

\(x(n) = 2Δ(n) + Δ(n - 1)y(n) = 2Δ(n) - Δ(n - 1) - Δ(n - 2)We know that y(n) = h(n) * x(n)or h(n) = y(n) / x(n)\)

Substituting the values of x(n) and y(n) in the above equation, we geth

\((n) = [2Δ(n) - Δ(n - 1) - Δ(n - 2)] / [2Δ(n) + Δ(n - 1\))]simplifying the above equation,

\(h(n) = [2 - 1/z^-1 - 1/z^-2] / [2 + 1/z^-1]\)Where, z^-1 is the time shift operator.Simplifying the above equation by taking\(LCM,h(n) = [2z^2 - z - 1] / [2z^2 + z]\)Solving the above equation using partial fraction decomposition method,\(h(n) = [3 / (2z)] - [1 / (z + 1/2)]\)Therefore,

\({h(n)} = [3 / 2, -1]\)with corresponding

n = [0, 1].Hence, the solution is given by

\(h(n) = [3 / 2, -1].\).

Therefore, the required value of\({h}(\mathrm{n}) is given by the expression \delta(n-1)+3\delta(n-2)-3\delta(n-3).\)

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Answer:

Yes, we agree with her prediction.

Step-by-step explanation:

Given:

Number of sample student = 60

Number of total student = 600

Number of student plan to go college = 675

Sample of student plan to go college = 75%

Find:

Prediction is correct or not

Computation:

Number of student plan to go college in sample = 60 × 75%

Number of student plan to go college in sample = 45

Number of student plan to go college = Number of student plan to go college in sample [900 / 60]

Number of student plan to go college = 45[900 / 60]

Number of student plan to go college = 45[15]

Number of student plan to go college = 675

So,

Yes, we agree with her prediction.

Answer:

\(a_{n}\) = 5n + 5

Step-by-step explanation:

The nth term of an arithmetic progression is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 10 and d = a₂ - a₁ = 15 - 10 = 5 , then

\(a_{n}\) = 10 + 5(n - 1) = 10 + 5n - 5 = 5n + 5

Ms. Martinez made 5 costumes for the members of the chorus in the school musical.

To find the number of costumes Ms. Martinez made, we need to divide the total amount of fabric she bought by the amount of fabric used per costume.

Ms. Martinez bought 11 1/4 yards of fabric, which can also be written as 11.25 yards.

Each costume requires 2 1/4 yards of fabric, or 2.25 yards.

To calculate the number of costumes, we divide the total fabric purchased by the fabric used per costume:

Number of costumes = Total fabric purchased / Fabric used per costume

Number of costumes = 11.25 yards / 2.25 yards

Number of costumes = 5

Therefore, Ms. Martinez made 5 costumes for the members of the chorus in the school musical.

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Answer:

the answer is A because the pair of ratios are equivalent.

To find dz/dt using the chain rule, we need to calculate the derivatives of z with respect to x and y separately, and then multiply them by the derivatives of x and y with respect to t.

Given:

z =  \(cosh^{2} (xy)\)

x = (1/2)t

y = \(e^{t}\)

Let's start by finding the partial derivatives of z with respect to x and y:

∂z/∂x = \(2cosh(xy) * sinh(xy) * y\)  (using the chain rule)

∂z/∂y = \(2cosh(xy) *sinh(xy)*x\)    (using the chain rule)

Next, let's find the derivatives of x and y with respect to t:

dx/dt = 1/2

dy/dt = \(e^{t}\)

Finally, we can use the chain rule to find dz/dt:

dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt)

      = \(2cosh(xy) *sinh(xy)*y*(1/2) + 2cosh(xy)*sinh(xy)*x*e^{t}\)

Now, substitute the given expressions for x and y:

\(dz/dt = 2cosh((1/2)t*e^{t} * sinh((1/2)t*e^{t} *(1/2)* + 2cosh((1/2)t*e^{t} *sinh((1/2)t*e^{t} *((1/2)t)\)

Simplifying further, we have:

\(dz/dt = cosh((1/2)t*e^{t} *sinh((1/2)t*e^{t})* e^{t} + cosh((1/2)t* e^{t}*sinh((1/2)t*e^{t}* ((1/2)t)\)

This is the expression for dz/dt using the chain rule with the given values of x and y.

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the gamma distribution becomes approximately normal due to the Central Limit Theorem when n is large.X ︽.Norm(a/λ, a/λ²) since it is an approximately normal distribution with mean a/λ and variance a/λ².

(a) Gamma random variables are sums of random variables, and as n gets large, the Central Limit Theorem applies. When n is large, the gamma random variable with parameters (n, λ) approaches a normal distribution, as the sum of independent and identically distributed Exponential(λ) random variables is distributed roughly as a normal distribution with mean n/λ and variance n/λ². In other words, the gamma distribution becomes approximately normal due to the Central Limit Theorem when n is large.

(b) The problem asks to show that:lim (1 + x/n)-n = e⁻x.The expression (1 + x/n)⁻ⁿ can be written as [(1 + x/n)¹/n]ⁿ. Now letting n → ∞ in this equation and replacing x with aλ yields the desired result from part (a):lim (1 + x/n)ⁿ

= lim [(1 + aλ/n)¹/n]ⁿ

= e⁻aλ(d)

The central limit theorem with continuity correction can be expressed as:P(Z ≤ z) ≈ Φ(z + 0.5/n)if X ~ B(n,p), where Φ is the standard normal distribution and Z is the standard normal variable.

This continuity correction adjusts for the error made by approximating a discrete distribution with a continuous one.(e) The exact probability that the walk is within 500 steps from the origin can be calculated by using the normal distribution. Specifically, we have that:

P(|X - a/λ| < 500)

= P(-500 < X - a/λ < 500)

= P(-500 + a/λ < X < 500 + a/λ)

= Φ((500 + a/λ - μ)/(σ/√n)) - Φ((-500 + a/λ - μ)/(σ/√n)),

where X ~ N(μ, σ²), and in this case, μ = a/λ and σ² = a/λ².

Therefore, X ︽.Norm(a/λ, a/λ²) since it is an approximately normal distribution with mean a/λ and variance a/λ².

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The sequence of transformations that show that the triangles are similar are given as follows:

b. Dilate triangle AED with center A by a scale factor of 2, then reflect over line AC.

c. Reflect triangle ABC over line AC, then dilate using center A with a scale factor of 1/2.

Similar triangles are triangles that share these two features listed as follows:

The transformations for this problem are given as follows:

When we apply the possible transformations, the two triangles would be one over the other, meaning that they are similar.

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In this context, a type I error would occur if the null hypothesis was rejected when it is actually true, meaning that the patient does not have the disease but is diagnosed with it.

This would be a false positive result. It is important to note that a type I error is related to the level of significance chosen for the hypothesis test, and it represents the probability of rejecting the null hypothesis when it is true.

In this case, if the level of significance was set at 0.05, for example, there would be a 5% chance of making a type I error. It is also important to consider the consequences of making a type I error in a medical context, as it could lead to unnecessary treatments or interventions that could harm the patient.

Therefore, it is crucial to carefully design hypothesis tests and choose appropriate levels of significance to minimize the risk of making such errors.

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Answer:

Make 7/5 and 1/8 have a common denominator, which is 40.

7/5 x 8/8 = 56/40(minutes driving to her home)

1/8 x 5/5 = 5/40 she spends

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer: A.

Step-by-step explanation:

The measure of angle ABP from the given circle is 90°.

From the given figure,

11) Measure of angle ABP is 90°.

12) Measure of angle BAK is 180°-(90°+25°)

= 180°-115°

= 65°

13) Measure of angle AQP is 90°.

14) Measure of angle QAK is 180°-(90°+25°) (Because ∠BPA=∠QPA=25°)

15) Measure of Arc BK = Measure of angle BAK = 65°

16) Measure of Arc BQ = Measure of angle BAQ = 65°×2

= 130°

17) m∠CAD=m∠BAK=65°

Therefore, the measure of angle ABP from the given circle is 90°.

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Answer: SA = 445.05

Step-by-step explanation:

The measure of the major arc JLK will be 206°. Then the correct option is B.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The measure of the minor arc JK will be 154°.

Then the sum of the major arc and minor arc in a circle is 360°.

Then the major arc JLK will be given as,

JLK + JK = 360°

JLK + 154° = 360°

JLK = 206°

The measure of the major arc JLK will be 206°. Then the correct option is B.

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(a) | Masses (kg) | Frequency | Cumulative Frequency |

|-------------|-----------|---------------------|

| 15-24       | 14        | 14                  |

| 25-34       | 54        | 68                  |

| 35-44       | 24        | 92                  |

| 45-54       | 26        | 118                 |

| 55-64       | 2         | 120                 |

(b) The cumulative frequency curve starts from the origin (0, 0) and moves upward and to the right, indicating that the mass of logs is increasing as we move right on the x-axis.

To construct the cumulative frequency table for the distribution of masses of 120 logs of wood, we need to add up the frequencies of each class and all the classes before it.

(b) To draw a cumulative frequency curve, we plot the cumulative frequency values against the upper class limits. The plot shows how the cumulative frequency increases with the increase in the mass of the log.

We use the same class intervals as in part (a):

- x-axis = Masses (kg)

- y-axis = Cumulative frequency

To plot the cumulative frequency curve, we mark the upper limit of each class on the x-axis, and its corresponding cumulative frequency on the y-axis. Then, we join the plotted points with a smooth curve, as shown in the graph.

The steeper the curve, the more rapid the increase in cumulative frequency, indicating that a larger number of logs fall in higher mass categories.

In the given distribution, the plot of the cumulative frequency curve shows that the majority of logs fall in the mass range of 25-34 kg, closely followed by the range of 45-54 kg.

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Answer:

300

Step-by-step explanation:

5²•(4+2³)

5²•(4+8)

5²•(12)

5²•12

25•12

300

Answer:

300

Step-by-step explanation:

Answer:

116π in

Step-by-step explanation:

Circumference = 2πr

Circumference = 2(58)π

Circumference = 116π

-Chetan K

To rewrite the integral ∫(2x)\(e^{4x^{2} }\)dx using integration by parts, we'll consider the function f(x) = (2x) and g'(x) = \(e^{4x^{2} }\).

Integration by parts states that ∫u dv = uv - ∫v du, where u and v are functions of x.

Let's assign:

u = (2x) => du = 2 dx

dv = \(e^{4x^{2} }\) dx => v = ∫\(e^{4x^{2} }\) dx

To evaluate the integral of v, we need to use a technique called the error function (erf). The integral cannot be expressed in terms of elementary functions. Hence, we'll express the integral as follows:

∫\(e^{4x^{2} }\) dx = √(π/4) × erf(2x)

Now, we can rewrite the integral using integration by parts:

∫(2x)\(e^{4x^{2} }\) dx = uv - ∫v du

= (2x) × (√(π/4) × erf(2x)) - ∫√(π/4) × erf(2x) × 2 dx

= (2x) × (√(π/4) × erf(2x)) - 2√(π/4) × ∫erf(2x) dx

The integral ∫erf(2x) dx can be further simplified using substitution. Let's assign z = 2x, which implies dz = 2 dx. Substituting these values, we get:

∫erf(2x) dx = ∫erf(z) (dz/2) = (1/2) ∫erf(z) dz

Therefore, the final expression becomes:

∫(2x)\(e^{4x^{2} }\) dx = (2x) × (√(π/4) × erf(2x)) - √(π/2) × ∫erf(z) dz

Please note that the integral involving the error function cannot be expressed in terms of elementary functions and requires numerical or tabulated methods for evaluation.

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I did 0.80-0.25=0.55

so I figured that is what she had left so I know took the total 0.80-0.55 and got0.25 which is B.

My friend said the correct answer was A.

Don't worry I just did this problem!

The distance Josh ran more in June than in July, if Josh ran 84.6 miles in June. In July, he ran 0.55 times this distance in June, is 38.07 miles.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

Josh ran 84.6 miles in June. In July, he ran 0.55 times this distance in June,

Calculate the distance covered in July = 0.55 × 84.6

Calculate the distance covered in July = 46.53 miles

Calculate the distance he ran more in June than in July = 84.6 - 46.53

The distance he ran more in June than in July = 38.07 miles

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The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given below.

⇒ x² + 2x + 1

Factorize the expression, then the factor of the expression will be

⇒ x² + x +  x + 1

⇒ x(x + 1)x + 1(x + 1)

⇒ (x + 1)(x + 1)

⇒ (x + 1)²

The product of two binomials will be (x + 1) and (x + 1).

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Answer:

\(172\frac{1}{2}\) gallons

Step-by-step explanation:

Considering she waters her plants with 25 1/2 gallons  i.e 51/2

and with the new system, she does it with 19 3/4 i.e 79/4

taking the difference:

\(\frac{51}{2} - \frac{70}{4}\) = \(\frac{23}{4}\) gallons per day

For 30 days:

30 x \(\frac{23}{4}\) = 172.5 or \(172\frac{1}{2}\) gallons