multiplying fractions
\(3 \frac{8}{9} \times 1 \frac{2}{3} \)
​

First we multiply 9 and 15, which is 135cm. 100cm = 1m so the plant will grow 1.35m, so the plant is now 9.35m

Step-by-step explanation:

Mohan said, "My brother arrived home late." (Change the sentence into reported speech).

Answer: 23100 voters

Step-by-step explanation:

42*55000=2310000

2310000/100=23100 voters

Answer:

Step-by-step explanation:

5. angle FDE = 180-90-63 = 27°

 arc FE = 2×27 = 54°

6. arc GJ = 360-68-31-115 = 146°

 angle GHJ = 146/2 = 73°

7. angle GIJ = 146/2 = 73°

8. arc DAB = 2×101 = 202°

 arc BCD = 360°-202 = 158°

 angle A = 158/2 = 79°

 angle B = 360-79-110-68 = 112°

10. see picture

5) The sum of angle in the triangle DEF is 180 degrees

mFE = <D

Recall that <D+<E+<F = 180⁰

<D+63+90 = 180

<D = 180-153

<D = 27 degrees

Hence the measure of arc FE is 27degrees

6) For this circle geometry, we will use the theorem

The sum of Opposite side of a cyclic quadrilateral is 180 degrees.

A + C = 180

m<A + 101 = 180

m<A = 180-101

m<A = 79degrees

Similarly

B + D = 180

m<B + 68 = 180

m<B = 180-68

m<B = 112degrees

7) The sum of angle in a circle is 360, hence;

arcGJ+68+31+115 = 36p

arcGJ = 360 - 214

arcGJ = 146⁰

Since the angle at the centre is twice angle at the circumference, then;

<GHJ = 1/2 arcGJ

<GHJ = 1/2(146)

<GHJ = 73⁰

<GHJ = <GIJ = 73⁰ (angle in the same segment of the circle are equal)

8) Recall that the sum of Opposite side of a cyclic quadrilateral is 180 degrees.

P + R = 180

57 + <R = 180

m<R = 180-57

m<R = 123degrees

Similarly, m<Q+m<S = 180⁰

Since the triangle in a semi circle is a right angled triangle, hence m<Q = 90 degrees (triangle PQR is a right angled triangle)

m<S = 180 - 90

m<S = 90 degrees

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9514 1404 393

Answer:

  (x, y) = (-1 2/9, 11 1/9)

Step-by-step explanation:

My favorite solution method is a graphing calculator. It shows the solution to this system of equations is ...

  (x, y) = (-1 2/9, 11 1/9)

__

When the solutions are not integers, sometimes solutions involving elimination or substitution get into arithmetic with fractions. Using matrix methods, such as Cramer's Rule can avoid that until the last step. Here, we'll use a "cross multiplication" method.

First we put both equations into general form.

  5x +y -5 = 0

  x +2y -21 = 0

Now, we consider the array of coefficients, with the first repeated as the last:

  5, 1, -5, 5

  1, 2, -21, 1

The differences of cross products of adjacent columns are ...

  d1 = (5)(2) -(1)(1) = 10 -1 = 9

  d2 = (1)(-21) -(2)(-5) = -21 +10 = -11

  d3 = (-5)(1) -(-21)(5) = -5 +105 = 100

The relation ...

  1/d1 = x/d2 = y/d3

specifies how these differences are used to find the solutions.

  x = d2/d1 = -11/9 = -1 2/9

  y = d3/d1 = 100/9 = 11 1/9

The solution is (x, y) = (-1 2/9, 11 1/9).

Answer:

none, because all of them are greater than -3

Answer:

The targeted population is USA residents who died of heart disease.

Step-by-step explanation:

According to this case, "the death rates due to heart disease among the smokers and nonsmokers are compared to see if smoking causes heart disease."  This implies that the study targets those USA residents who died of heart disease to find out if the cause of death can be traced to heart disease caused by smoking or not.  The main concentration for the study defines the targeted population.  It is this group of residents who died of heart disease that is the population of interest.  This means that the targeted population is a certain group of the population that share similar characteristics, especially death resulting from heart disease caused by smoking.

Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.

Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

Answer:

y = 10.5x - 8.25

Step-by-step explanation:

m = (44.25 - 12.75)/(5 - 2) = 10.5

y = mx + b

y = 10.5x + b

12.75 = 10.5 × 2 + b

b = -8.25

y = 10.5x - 8.25

Answer:

Units of measure:-

Yard

Foot

Pound

Kilogram

Mile

Meter

Quart

Things to measure:-

Age

Circumference

Radius

Distance

Perimeter

Area

Temperature

Length

Width

Tools for measurement:-

Tape measure

Ruler

Thermometer

Cup

Scale

Step-by-step explanation:

For the remaining set of garments, the average per day that they need to be completed would be = 126 sets/day.

The quantity of garments planned to be made by the factory = 690sets.

The rate of coverage for 5 days = 75sets/day.

That is for 5 days the number of garments covered = 75×5 = 375

The remaining sets = 690-375 = 315

The average per day to cover the remaining sets of garment = 315/2.5 = 126 sets/day

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Answer:

153250

Step-by-step explanation:

153250

Answer:16feet

Step-by-step explanation:

The explanation is in the attached file

Answer:

(2,3) (4,2) (5,2) (1,4) (0,2)

Step-by-step explanation:

because all these points have something common to each other. Now pay attention in your class and stop cheating!!

Answer:

Step-by-step explanation:

eq. of circle is (x-2)²+(y-3)²=10²

now substitute the values of x and y

which satisfies the above eq.that point lies on the circle.

Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°

The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.

Now, for the transverse line theorem we can say that:

Angle 1 will be composed of two angles namely:

48 degrees and (180 - 153) degrees.

Thus:

m∠1 = 48° + 27°

m∠1 = 75°

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Since the ratio of boys to girls is 5:4 and there are 60 girls, let b be the number of boys and g be the number of girls. Then:

Therefore, there are 75 boys in the choir.

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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Answer:

14.1 cm

Step-by-step explanation:

Answer:

9² and 10²

Step-by-step explanation:

9² = 81

10² = 100

100 - 81 =19

Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

Answer:

Step-by-step explanation:

To simplify the expression 3 x (3/4) whole to a unit fraction, we can start by multiplying the whole number 3 by the denominator of the fraction, which is 4:

3 x (3/4) = (3 x 4)/4 x (3/4) = 12/4 x 3/4

We can simplify the fraction 12/4 by dividing both the numerator and denominator by 4:

12/4 = 3

Substituting this back into the expression, we have:

3 x (3/4) = 3/1 x (3/4) = 9/4

Therefore, 3 x (3/4) whole is equal to the unit fraction 9/4.

Answer:

ummmmmwm whatttt

Step-by-step explanation:

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The three statistical questions are: A. How many hours of sleep per night do students usually get when they have school the next day? B and E.

A statistical question is one that may be resolved via the collection and examination of data. The question frequently incorporates a variable that might differ from person to person or scenario to situation, and the solution is not always the same. The words "how many," "what is the average," "what is the range," "what is the distribution," etc. are frequently used in statistical queries.

The three statistical questions are:

How many hours of sleep per night do students usually get when they have school the next day?

What are the heart rates of the students in Mr. Peterson's physical education class?

How many runs did the New York Yankees score in their last game?

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Answer:

a) Hence the endpoints of a t-distribution with 5% beyond them in each tail if the sample has size n=12 is ± 1.796.

b) Hence the endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20 is ± 2.539.

Step-by-step explanation:

Here the answer is given as follows,

Answer:

f(x) \(\leq\) 3x + 4

g(x)  ≥ -1/2x - 5

Step-by-step explanation:

Point D is below f(x)  and above g(x)

Helping in the name of Jesus.

Answer:

6400

Step-by-step explanation:

This is a simple Arithmetic Progression.

First term (a) = 1

Number of terms (n) = 80

Difference between 2 consecutive terms (d) = 2

Now we can use the formula.

On solving this, you'll get

Sum =  6400

I hope this helps!

The required sum of the first 80 positive odd integers. is 6400.

Arithmetic progression is the series of numbers that have common differences between adjacent values is equal.

For odd arithmetic progression

The first term, a = 1

Number of terms = 80

Difference between terms d = 2

Now we can use the formula.
sum =  n/2[2a + (n - 1)d]

sum = 80 /2 [2 × 1 + (80 - 1)2]
Sum = 40 [160]

Sum =  6400

Thus, the required the sum of the first 80 positive odd integers. is 6400.

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The number of points to be removed from the graph is 2

from the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we can see that

2 points have the same y coordinates

Another 2 points have the same y coordinates

For it to be a function, one of the 2 points must be removed each

So, we have the number of points to be removed from the graph is 2

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Answer:

Please check the explanation.

Step-by-step explanation:

Part 1)

5x + 9y, when x=8, y=11

substituting x=8, y=11 in 5x + 9

5x + 9y = 5(8) + 9(11)

            = 40 + 99

            = 139

Part 2)

a³ –c + b, when a=3, b=6, c=8

substituting a=3, b=6, c=8 in a³ –c + b

a³ –c + b = (3)³ - 8 + 6

               = 27 - 2

               = 25

Part 3)

4(g –h) +10, when g=12, h=7

substituting g=12, h=7 in 4(g –h) +10

4(g –h) +10 = 4(12 - 7) + 10

                  = 4(5) + 10

                  = 20 + 10

                  = 30

Part 4)

k³ –4j +12, when k=8, j=2

substituting k=8, j=2 in k³ –4j +12

k³ –4j +12 = (8)³ - 4(2) + 12

                 = 512 - 8 + 12

                 = 516

Summary: