what does angle DFE= in degrees?
Type only number for answer​

Answer:

12 = 2 × 2 × 3

48 = 3 × 2 × 2 × 2 × 2

60 = 3 × 2 × 5 × 2

Thus HCF = 2 × 2× 3 = 12

Answer: the answer is 12 hope it helps

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

5/2x = 1

2/5 x 5/2x = 1 x 2/5

x = 2/5

Answer:

x = 2/5

Explanation:

Step 1: Multiply both sides by 2/5.

(2/5) * (5/2x) = (2/5) * (1)

x = 2/5

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

Work Shown:

0.001 = 1/1000

Apply the cube root to both parts of 1/1000 to get

\(\sqrt[3]{1} = 1\\\\\sqrt[3]{1000} = 10\)

So this means that, \(\left(\frac{1}{10}\right)^3 = \frac{1}{10}*\frac{1}{10}*\frac{1}{10} = \frac{1}{1000} = 0.001\)

Having a side length of 1/10 = 0.1 unit leads to a volume of 0.001 cubic units.

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

A shortcut alternative is to use your calculator to get

\((0.001)^{1/3} = 0.1\)

The exponent of 1/3 is the same as a cube root.

The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

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Answer:

the simplest form is ⅓...............

Removing the electric car from the data set will reduce the standard deviation as the extreme value of 112 mpg is taken out, resulting in a decrease in the spread of the data. The interquartile range (IQR) will also be affected as the extreme outlier is taken out, will decrease the spread of the data in the boxplot.

The electric car with a rating equivalent to 112 miles per gallon is an extreme outlier, which means it is very far from the rest of the data. Therefore, removing this outlier from the data set will decrease the variability and, consequently, decrease the standard deviation. The extreme outlier with the rating equivalent to 112 miles per gallon is outside of the whiskers of the boxplot, which means it is beyond the range of the middle 50% of the data. Therefore, removing this outlier from the data set will decrease the spread of the data in the boxplot and, consequently, decrease the IQR.

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1. HP price for Susie is R 282600 and David is R 179300

2. The difference between the total price paid by Susie and David  is R 103300

3. The interest that Susie and David have to pay as a percentage of the cash price​ is 117.38% and 37.92%

The HP price, also known as the hire purchase price, is the total amount that a buyer pays for a product when purchasing it through a hire purchase agreement.

It includes the cash price of the product plus any interest and fees charged by the lender.

Here we have

3.1.1, For Susie:

The cash price of the car is R 130000.

She pays a 10% deposit, which is:

= [10/100] × 130000 = R 13000

=> HP price =  the cash price - the deposit

=>  130000 -  13000 = R 117000

She will pay monthly installments of R 4600 for 3 years,

which is 36 months.

Therefore, the total amount she will pay is:

36 x 4600 = R 165600

Therefore, the total amount she will pay is R 165600

The HP price for Susie is,  

117000 + 165600 = R 282600

For David:

The cash price of the car is R 130000. He pays a 35% deposit, which is:

=> [ 35/100] × 130000 = R 45500

The HP price = 130000 - 45500 = 84500

He will pay monthly installments of R 3950 for 2 years, which is 24 months. Therefore, the total amount he will pay is:

24 × 3950 = 94800

The HP price for David is, therefore:

=> 84500 + 94800 = R 179300

3.1.2, The difference between the total price paid by Susie and by David  

=  282600 - 179300 = R 103300

3.1.3

For Susie:

The total interest she has to pay is the difference between the HP price and the cash price, which is:

=> 282600 - 130000 = R 152600

The interest rate as a percentage of the cash price is:

=> (152600/130000) × 100% = 117.38%

For David:

The total interest he has to pay is the difference between the HP price and the cash price, which is:

=> 179 300 - 130 000 = R 49 300

The interest rate as a percentage of the cash price is:

=> (49 300/130000) × 100% = 37.92%

Therefore,

1. HP price for Susie is R 282600 and David is R 179300

2. The difference between the total price paid by Susie and David  is R 103300

3. The interest that Susie and David have to pay as a percentage of the cash price​ is 117.38% and 37.92%

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The value of \(z_{\alpha /2}\) that corresponds to a 90% confidence interval is

The confidence level is the likelihood that, if you repeat your experiment or resample the population in the same manner, you will come close to arriving at the same estimate.

The estimate's upper and lower bounds are what make up the confidence interval for a particular level of confidence.

For 90%confidence interval = 0.9

significance level, α = 1 - 0.9 = 0.10

For two tailed test, α/2 = 0.05

using z table

0.0505 = -1.64

0.05 = x

0.0495 = -1.65

solving for x by interpolation

(0.0505 - 0.05) / (0.05 - 0.0495) = (-1.64 - x) / (x - -1.65)

0.0005(x + 1.65) = 0.0005(-1.64 - x)

x + x = -1.64 - 1.65

x = -1.645

from z tables at 90% confidence interval in two tailed test the score is found to be 1.645

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Answer: x >-2

Step-by-step explanation:

3x+8>x+4

2x+8>4

2x>4-8

2x>-4

x>-4/2

x>-2

Answer: C

Step-by-step explanation:

Answer:

C. $0.22 per box

Step-by-step explanation:

if it's two juice boxes and they cost $0.44 together. You divide by two, since there are two boxes. with that you get your answer, 44÷2=22. making the answer $0.22

The equation (v²* r) / (2g) represents the object's mass, m.

To solve for the object's mass, m, in the equation v = (2gm)/r, we can rearrange the equation to isolate the variable m.

1. Start with the equation v²= (2gm)/r.
2. Multiply both sides of the equation by r to eliminate the denominator: v² * r = 2gm.
3. Divide both sides of the equation by 2g: (v² * r) / (2g) = m.

The equation (v²* r) / (2g) represents the object's mass, m. This is the  answer to the question.

To further understand the equation, let's break it down. The equation v² = (2gm)/r is derived from the principle of escape velocity, which is the minimum velocity needed for an object to escape the gravitational pull of the Earth.

In the equation, v represents the velocity of the object, r is the distance from the center of the Earth to the object, and g is the acceleration due to gravity. The constant g is approximately 9.8 m/s².

By solving for the object's mass, we can determine the mass required for the object to have a specific velocity at a given distance from the Earth's center.

In conclusion, to find the object's mass (m) in the equation v² = (2gm)/r, you can use the formula (v² * r) / (2g). This equation allows you to calculate the mass of an object required to achieve a certain escape velocity at a given distance from the Earth's center.

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The volume of a sphere with radius 8 units is 2143.57 units³

What is a Sphere?

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the volume of the sphere be represented as A

Now , the value of A is

Let the radius of the sphere be r

The value of r = 8

Now , the formula to calculate the volume of the sphere is

Volume of a Sphere = ( 4/3 ) πr³

Substituting the values in the equation , we get

Volume of a Sphere = ( 4/3 ) x 3.14 x 8 x 8 x 8

Volume of a Sphere = ( 4/3 ) x 3.14 x 512

Volume of a Sphere = ( 4/3 ) x 1607.68

Volume of a Sphere = 2143.57 units³

Therefore , the value of A is 2143.57 units³

Hence , the volume of the sphere is 2143.57 units³

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Answer:

yes

Step-by-step explanation:

3+3=6

6+6=12

so yes, that statement is correct

Answer: yes this statement is completely correct.

Step-by-step explanation:

The Lagrange polynomial basis L = {l0(t), l1(t),..., ln(t)} is a set of polynomials with specific properties: li(t_i) = 1 for all i = 0, 1,..., n, and li(t_j) = 0 for all i, j = 0, 1,..., n, where i ≠ j. This basis allows you to represent any polynomial p(t) in Pr by a linear combination of the Lagrange polynomials in the basis L.

Polynomials are mathematical expressions consisting of variables and coefficients, often used in algebra and calculus. In this context, we are considering polynomials of degree n or less, denoted by Pr.

Lagrange polynomials are a type of polynomial that form a basis for Pr. This means that any polynomial in Pr can be expressed as a linear combination of the Lagrange polynomials. The Lagrange polynomial basis is formed from a set of n + 1 distinct points in R, denoted {to, t1, ..., tn}.

Each Lagrange polynomial, denoted li(t), has the following properties:
- li(ti) = 1 for all i = 0, 1,..., n
- li(tj) = 0 for all i, j = 0, 1,..., n, i + j.

In other words, each Lagrange polynomial is equal to 1 at its corresponding point ti, and is equal to 0 at all other points. These properties ensure that the Lagrange polynomials are linearly independent and form a basis for Pr.

Hope this helps! Let me know if you have any further questions.
Hi! I'd be happy to help you with your question. Polynomials are mathematical expressions involving a sum of powers in one or more variables multiplied by coefficients. The Lagrange polynomial is a specific type of polynomial that provides a way to interpolate a polynomial function using a set of n + 1 distinct points in R, {t0, t1, ..., tn}.

The Lagrange polynomial basis L = {l0(t), l1(t),..., ln(t)} is a set of polynomials with specific properties: li(t_i) = 1 for all i = 0, 1,..., n, and li(t_j) = 0 for all i, j = 0, 1,..., n, where i ≠ j. This basis allows you to represent any polynomial p(t) in Pr by a linear combination of the Lagrange polynomials in the basis L.

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Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

The value of r in terms of l and h is,

⇒ r = √((l/2)² + h²)

Now, We can use the Pythagorean theorem to relate r, l, and h as,

Since, The chord of the circle divides the circle into two segments, each with a height of h.

Let's call the segments are A and B.

Then, the length of the chord (l) is equal to the sum of the bases of segments A and B.

Therefore, the length of each base is,

(l/2).

Hence, We can use the Pythagorean theorem to relate r, l/2, and h for one of the segments as;

⇒ r² = (l/2)² + h²

⇒ r = √((l/2)² + h²)

Thus, The value of r in terms of l and h is,

⇒ r = √((l/2)² + h²)

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Answer:

The determinant of J can be found using the formula ad - bc

where   \(\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\)

So we have \(-2 * 5 - 6 * 3 = -10 - 18 = -28\)

Step-by-step explanation:

The value of |J| is 28.

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array.

Given:

J=[−2365].

now, determinant of the matrix J is

|J|= |(-2) * 5 - 3*6|

|J|= |-10 - 18|

|J|= |-28|

|J|= 28

hence, the value of |J|  is 28.

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Answer:

566.25

Step-by-step explanation:

515.95×9.75%=50.30

515.95+50.30=566.25

Sarah's charges per hour for working during the week will be $9.5.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.

Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be

45x + 5y = 902.5           ...1

50x + 10y = 1045

25x + 5y = 522.5          ...2

Subtract equation 2 from equation 1, then we have

45x - 25x = 902.5 - 522.5

20x = 380

x = 19

And the value of y will be

25 (19) + 5y = 522.5

475 + 5y = 522.5

5y = 47.5

y = 9.5

Sarah's charges per hour for working during the week will be $9.5.

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1.1 The relationship between sampling distribution and confidence interval is that the sampling distribution helps us understand the distribution of sample statistics (such as the sample mean or proportion) when repeatedly sampling from a population.

The confidence interval, on the other hand, provides a range of values within which we can be confident that the true population parameter lies based on the sample data.

In other words, the sampling distribution gives us information about the variability and distribution of sample statistics, while the confidence interval uses this information to estimate the range of likely values for the population parameter.

1.2 To calculate the probability that the sample mean is between 9.0 and 11.0, we need to standardize the values using the z-score formula and then look up the corresponding probabilities from the standard normal distribution.

First, calculate the z-scores:

z1 = (9.0 - 10) / (3 / √40) = -1.8257

z2 = (11.0 - 10) / (3 / √40) = 1.8257

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the sample mean is between 9.0 and 11.0 can be calculated as the difference between the two probabilities:

P(9.0 < x < 11.0) = P(z1 < Z < z2)

1.3 (a) To calculate the probability that the percentage of voters who support the candidate is between 40% and 45% in a sample of 200 voters, we can use the sampling distribution of sample proportions. Assuming the sample proportion follows a normal distribution, we can standardize the values using the z-score formula and then calculate the corresponding probabilities.

First, calculate the z-scores:

z1 = (0.40 - 0.40) / √[(0.40 * (1 - 0.40)) / 200] = 0

z2 = (0.45 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is between 40% and 45% can be calculated as the difference between the two probabilities:

P(40% < p < 45%) = P(z1 < Z < z2)

(b) To calculate the probability that the percentage of voters who support the candidate is more than 50%, we can again use the sampling distribution of sample proportions. We standardize the value using the z-score formula and calculate the corresponding probability.

Calculate the z-score:

z = (0.50 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Look up the probability associated with this z-score using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is more than 50% can be calculated as:

P(p > 50%) = P(Z > z)

1.4 To determine the 95% confidence interval for the true mean resistance, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, calculate the standard error:

Standard Error = population standard deviation / √(sample size)

              = 0.35 / √10

Next, find the critical value corresponding to a 95% confidence level from a t-distribution table with 9 degrees of freedom (n-1). The critical value for a 95% confidence level is approximately 2.

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To find h'(3) given h(x) = f(x) xg(x), we use the product rule of differentiation:

h'(x) = f'(x) xg(x) + f(x) g(x) + f(x) xg'(x)

We are not given the functions f(x) and g(x), but we can use the given graphs to estimate their values near x = 3. Let's say that f(3) = 2 and g(3) = 5. We also need to estimate f'(3) and g'(3) in order to calculate h'(3). We can estimate these values using the slopes of the tangent lines to the graphs at x = 3.

Let's say that the slope of the tangent line to the graph of f(x) at x = 3 is 1, and the slope of the tangent line to the graph of g(x) at x = 3 is 3. Then we have:

f'(3) ≈ 1

g'(3) ≈ 3

Substituting these values into the product rule for h'(x), we get:

h'(x) = f'(x) xg(x) + f(x) g(x) + f(x) xg'(x)

h'(3) = f'(3) 3 g(3) + f(3) g(3) + f(3) 3

h'(3) = (1)(3)(5) + (2)(5) + (2)(3)

h'(3) = 19

Therefore, h'(3) is approximately equal to 19, based on the given graphs and our estimates of f'(3) and g'(3).

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When s = 0, it will take 20 units of time for the account to double to 2X.

(a) When s = 0, it means the deposit is made at time t = 0. We want to find the time it takes for the account to double to 2X.

To find this time, we need to solve the equation a(t) = 2, where a(t) is the accumulation function.

1 - 0.05t = 2

Simplifying the equation, we have:

-0.05t = 1

Dividing both sides by -0.05, we get:

t = -1 / (-0.05)

t = 20

Therefore, when s = 0, it will take 20 units of time for the account to double to 2X.

(b) When s = 5, it means the deposit is made at time t = 5. We want to find the time it takes for the account to double to 2X.

Using the same equation a(t) = 2 and substituting t = 5, we have:

1 - 0.05(5) = 2

1 - 0.25 = 2

0.75 = 2

This equation is not satisfied, which means the account will not double to 2X when the deposit is made at time t = 5.

(c) The answer in (a) is greater than the answer in (b) because when the deposit is made at time t = 0, the account has more time to accumulate interest and grow compared to when the deposit is made at time t = 5. As time progresses, the effect of compounding becomes more significant, and starting earlier allows for more growth and a shorter time to double the account.

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The domain of the following function: R: [(3,5), (8,6), (2,1), (8,6) is D. [2,3,8]

A function in mathematics is a relationship between two sets of values known as the domain and the range that allots a different element of the range to each element of the domain. A function, then, is a rule that links each input value (also known as an independent variable) to a corresponding output value (also called dependent variable).

Typically, the x-variable represents the input values while the y-variable represents the output values. A function is represented by the notation f(x), where x is the input variable and f is the name of the function. The domain of a function is the set of all possible input values.

Thus,

x-coordinates are: 3, 8, and 2.

Therefore, the domain of the function is D. [2,3,8]

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\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 500e^{0.07\cdot 10} \implies A \approx 1006.88\)

m=3*-1^2-(-1)-7

m=-9-(-1)-7

m=8-7

m=1

Answer:

:Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded

Step-by-step explanation:

Answer:  Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded to the nearest hundreth.

Step-by-step explanation:

Answer:

x=-2 y=-5

x=5 x=2

Answer:

x = 175

Step-by-step explanation:

Add 8 on both sides to get 350 = 2x.  Divide 2 on both sides to get your x value which is 175.

Answer:

I think is the last answer 6 < x