Divide $70 in these ratios 8:5:1

Answer:

Step-by-step explanation:

\(80.54=80+0.54=80+\frac{54}{100} =80+\frac{27}{50} =80\frac{27}{50}\)

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Answer:

False

Step-by-step explanation:

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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The probability of landing on the red shaded circle is 6/18

Probability simply measures the chances at which an event could occur in a sample or population.

Mathematically, Probability is calculated thus:

Here ,

P(red circle ) = 6/18

Therefore, the probability is 6/18

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Humanity would achieve a life expectancy of 110 years in approximately 60 years.

To calculate the number of years it would take for humanity to achieve a life expectancy of 110 years, we need to determine the number of decades required to reach this goal based on the given rate of increase.

In 2009, the life expectancy was about 80 years. From that point, we need to calculate the difference between the current life expectancy and the target life expectancy of 110 years.

110 years - 80 years = 30 years

Since the rate of increase is 5.3 years every decade, we can divide the difference by the rate to determine the number of decades required:

30 years / 5.3 years per decade ≈ 5.66 decades

Since we can't have a fraction of a decade, we need to round up to the nearest whole number. Therefore, it would take approximately 6 decades for humanity to achieve a life expectancy of 110 years.

To calculate the number of years, we multiply the number of decades by 10:

6 decades * 10 years per decade = 60 years

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According to the concept of compound interest, the effective annual yield on your investment of $1800 at a 6.3% interest rate compounded daily is 6.49%.

To find the effective annual yield, we need to use the formula for compound interest:

A = P(1 + r/n)ⁿˣ

Where A is the amount of money at the end of the investment period, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.

In this case, we know that the principal amount P is $1800, the annual interest rate r is 6.3%, and the interest is compounded daily, which means that n is 365 (the number of days in a year). We need to find the effective annual yield, which is the total amount of interest earned in one year.

To calculate the effective annual yield, we can use the following formula:

Effective Annual Yield = (1 + r/n)ⁿ - 1

Plugging in the values, we get:

Effective Annual Yield = (1 + 0.063/365)³⁶⁵ - 1

Effective Annual Yield = 0.0649 or 6.49%

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Answer:

K.E = 1/2mv²

Kinetic energy

Answer:

10 hours at job (1)

2 hours at job (2)

Step-by-step explanation:

As per the given information, one earns ($8) dollars at one of their jobs, and ($10) hours at the other. One must earn a total of ($100) dollars, and can work no more than (12) hours. Let (x) be the hours worked at job 1 and (y) be the hours worked at job two.

Since one can work no more than (12) hours, the sum of (x) and (y) must be (12), therefore the following equation can be formed;

\(x+y=12\)

One earns ($8) dollars at one of their jobs and ($10) at the other, but one earns a total of (100) one can form an equation to represent this situation.  Multiply the hours worked by the money earn per hour for each job, add up the result and set it equal to (100).

\(8x+10y=100\)

Now set up these equations in a system;

\(\left \{ {{x+y=12} \atop {8x+10y=100}} \right.\)

Use the process of elimination to solve this system. The process of elimination is a method of solving a system of equations. One must first manipulate one of the equations in the system such that one of the variable coefficients is the additive inverse of the other. That way, when one adds the equation, the variable cancels, one can solve for the other variable then back solve to find the value of the first variable,

\(\left \{ {{x+y=12} \atop {8x+10y=100}} \right.\)

Manipulate,

\(= \left \{ {{(*-8)(x+y=12)} \atop {8x+10y=100}} \right.\\\\\)

Simplify,

\(= \left \{ {{-8x-8y=-96} \atop {8x+10y=100}} \right.\\\)

Add,

\(=2y=4\)

Inverse operations,

\(y=2\)

Backsolve for (x), use equation one to achieve this,

\(x+y=12\\\)

Substitute,

\(x+2=12\)

Inverse operations,

\(x=10\)

Answer: C . Distributive property.

Step-by-step explanation:

5(x + 7) = 5x + 35  

You distribute 5(x+7) to get 5x + 35.

5* x = 5x

5*7 = 35  

If you add them you get 5x + 35

Answer:

third choice : Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.

You’re welcome ;)

Answer:

the third one will be it

Step-by-step explanation:

Move all terms that don't contain x to the right side and solve.

The Four-fifths is equal to ten-sixteenths of a number is x=32/25.

Given the statement is four-fifths is equal to ten-sixteenths of a number.

A mathematical statement is a meaningful component of words that can be  true or false. Simply, they are known as a statement.

Let us assume the given number be x.

According to the given statement,

Four fifths means 4/5.          ......(1)

And ten sixteenths means 10/16.

It is also given that ten sixteenths of a number means is (10/16)x.      .......(2)

Now, we will equate equation (1) and equation (2) according to the given statement is

4/5=(10/16)x

Further, we will cross multiply both sides, we get

4×16=10x×5

64=50x

Now, we will divide both sides by 50, we get

64/50=50x/50

64/50=x

32/25=x

Hence, the number for the given statement "Four fifths is equal to ten sixteenths of a number" is 32/25.

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It is noticed that the factors then the x-intercepts are the same value as that of factors.

Given that, the quadratic equation represented on the graph in factored form is y=(x-3)(x+2).

From the graph, x-intercepts are x=-2 and x=3.

The vertex of the given quadratic graph is (0.5, -6)

Therefore, it is noticed that the factors then the x-intercepts are the same value as that of factors.

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The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Answer: A. 0.01

Step-by-step explanation:

Type I error are refered to as false positives and it means that when a statistically significant difference is validated by the researcher even though the results aren't statistically significant.

Type I error is when one rejects the null hypothesis even though it's actually true. In this case, the inspector rejects the hypothesis which was that the proportion of water that is contained the product is 0.5.

The probability of type 1 error will then be equal to the hypothesis level of significance and this will be 0.01.

Answer:

D)      \(\sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1} )^{2} }\)

Step-by-step explanation:

Explanation:-

Let ( x₁, y₁) and ( x₂, y₂) be the two points

Distance formula

    d =      \(\sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1} )^{2} }\)

The balance in the account after the given period is \(\$6,872.74\)  

we know that

The compound interest formula is equal to  

\(\text{A}=\text{P}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}\)

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

\(\text{t}= 8 \ \text{years}\)

\(\text{P}=\$4,000\)

\(\text{r}=0.07\)

\(\text{n}=1\)

substitute in the formula above

\(\text{A}=\$4,000(1+\frac{0.07}{1})^{1\times8}=\$6,872.74\)  

Answer:

11 + 24x

Step-by-step explanation:

8 - 4(x - 7x) + 3

8 - 4x + 28x + 3

11 - 4x + 28x

11 + 24x

Answer:

8-4x+28x+3 = 24x+11

Step-by-step explanation:

brainliest?

Answer:

\(\boxed{ \bold{ \huge{ \boxed{ \sf{5}}}}}\)

Step-by-step explanation:

Given data : 6 , 3 , 2 , 1 , 9 , 9

Σfx = 6 + 3 + 2 + 1 + 9 + 9 = 30

N ( total number of observation ) = 6

Finding the mean

\( \boxed{ \sf{mean = \frac{Σfx}{N} }}\)

\( \dashrightarrow{ \sf{mean = \frac{30}{6} }}\)

\( \dashrightarrow{ \sf{mean = 5}}\)

Hope I helped!

Best regards! :D

Answer:

bce

Step-by-step explanation:

i just did it

Answer:

B, C, E

Step-by-step explanation:

Hope this helps <3

Shopping List: FRUIT, SALAD ( only Diced tomatoes) (and More like apple Pineapple

The equation we can use to find d, the total length of Alicia's trip in miles, is: 260 = (4/5)d

Let d be the total length of Alicia's trip in miles. According to the problem, the distance she drove to visit her grandparents is 4/5 of the total distance, so we can write:

260 = (4/5)d

To find the total distance d, we can solve this equation for d. First, we can multiply both sides by 5/4 to isolate d:

260 x 5/4 = (4/5)d x 5/4

325 = d

Therefore, the equation we can use to find d, the total length of Alicia's trip in miles, is: 260 = (4/5)d and the distance is d = 325

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3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer:

Expected benefit under this policy = $ 2694

Step-by-step explanation:

Given - An insurance policy on an electrical device pays a benefit of

            4000 if the device fails during the first year. The amount of the

            benefit decreases by 1000 each successive year until it reaches 0.

            If the device has not failed by the beginning of any given year, the

            probability of failure during that year is 0.4.

To find - What is the expected benefit under this policy ?

Proof -

Let us suppose that,

The benefit = y

Given that, the probability of failure during that year is 0.4

⇒Probability of non-failure = 1 - 0.4 = 0.6

Now,

If the device fail in second year , then

Probability = 0.6×0.4

If the device fail in third year, then

Probability = 0.6×0.6×0.4 = 0.6² × 0.4

Going on like this , we get

If the device is failed in n year, then

Probability = 0.6ⁿ⁻¹ × 0.4

Now,

The probability distribution is-

Benefit , x       4000       3000             2000            1000              0

P(x)                 0.4         0.6×0.4         0.6² × 0.4     0.6³ × 0.4     1 - 0.8704

                      (0.4)       (0.24)            (0.144)         (0.0864)       (0.1296)

At last year, the probability = 1 - (0.4+ 0.24+ 0.144+ 0.0864) = 1 - 0.8704

Now,

We know that,

Expected value ,

E(x) = ∑x p(x)

       = 4000(0.4) + 3000(0.24) + 2000(0.144) + 1000(0.0864) + 0(0.1296)

       = 1600 + 720 + 288 + 86.4 + 0

       = 2694.4

⇒E(x) = 2694.4 ≈ 2694

∴ we get

Expected benefit under this policy = $ 2694

The actual amount the salesman pays for an article with a marked price of N950.00 is N2,312.50.

Amount is a word used to refer to a quantity or amount of something. It can also be used to refer to the total sum of money, goods, or services due for payment or exchange. It can also refer to the balance of money or goods due for payment or exchange. Amount is also used to refer to the size, extent, or magnitude of something.

To calculate this amount, we first need to calculate the amount of discount the salesman is offering. This is calculated by taking the marked price and multiplying it by the discount percentage: N950.00 x 125% = N1,187.50. Then, we subtract this discount amount from the marked price: N950.00 - N1,187.50 = N2,312.50. This is the actual amount the salesman pays for the article.

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The maximum whole number of gigabytes of data Mamadou can use is 4.

The relation between two unequal expressions is defined as inequality.

Given that, Mamadou has to pay $52 per month and $3 per gigabyte.

Let Mamadou uses x gigabytes in a month, then the total cost is:

52 + 3x

Since the total cost should be under $65 per month, it follows:

52 + 3x < 65

3x < 65 - 52

3x < 13

x < 13/3

x < 4.33

Therefore, the maximum whole number of gigabytes of data Mamadou can use is 4.

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Answer and Explanation:

The Prolog rule expresses that logical implication (:-) describes the relationship between facts.

Prolog expressions are containing truth-functional symbols, which have the same intervention as in predicate calculus.

For example:  

English Predicate calculus prolog

and ^ ,

or v ;

By using information, given in the question,

We can make prolog:

Grandfather(X, Y)  :-mother(M,Y), father(X,M); father (F, Y), father(X,F)

Prolog (:- ) means define,

Prolog (,) represents a conjunction

And

Prolog (;) represent a disjunction

Answer:

the length is 18

Step-by-step explanation:

Answer:

Hello!

The length of XY is 18

Hope this helps!!