Solve the given system by the substitution method.
3x + y = 14
7x - 4y = 20​

Answer:

Answer:

The correct answer is:

(a) 0.0884

(b) 0.0190

(c) 0.9596

(d) 0.2921

Step-by-step explanation:

(a)

= [tex]P(1.26<Z<2.16)[/tex]

= [tex]P(Z<2.16)-P(Z<1.26)[/tex]

= [tex]0.9846-0.8962[/tex]

= [tex]0.0884[/tex]

(b)

= [tex]P(2.05<Z<3.05)[/tex]

= [tex]P(Z<3.05)-P(Z<2.05)[/tex]

= [tex]0.9989-0.9798[/tex]

= [tex]0.0190[/tex]

(c)

= [tex]P(-2.05<Z<2.05)[/tex]

= [tex]P(Z<2.05)-P(Z<-2.05)[/tex]

= [tex]0.9798-0.0202[/tex]

= [tex]0.9596[/tex]

(d)

= [tex]P(Z>0.55)[/tex]

= [tex]1-P(Z<0.55)[/tex]

= [tex]1-0.7088[/tex]

= [tex]0.2912[/tex]

Answer:

As for metric prefixes, "hecto" means hundred and "centi" means hundredth.  

So, converting .53 hectograms to centigrams requires multiplying it by 10,000.

So, .53 hectograms * 10,000 equals 5,300 centigrams.

Source http://www.1728.org/convprfx.htm

Step-by-step explanation:

Answer:

the answer is 32.8in.

Step-by-step explanation:

(sin 22)/42 = (sin 24)/x

x = 45.60

sin 46 = x/45.60

x = 32.80

32.8in.

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Answer:

[tex](a)\ Area = 13.0695[/tex]

[tex](b)\ Area = 26.139[/tex]

Step-by-step explanation:

Given

The attached image

Solving (a): The area (one side up)

This is calculated as:

Area= Area of semicircle + Area of rectangle

So, we have:

[tex]Area = \pi r^2 + l *w[/tex]

Where:

[tex]l,w =2,3[/tex] --- the rectangle dimension

[tex]d = 3[/tex] --- the diameter of the semicircle

So, we have:

[tex]Area = \pi * (3/2)^2 + 2 * 3[/tex]

[tex]Area = \pi * 2.25 + 6[/tex]

[tex]Area = 2.25\pi + 6[/tex]

[tex]Area = 2.25*3.142 + 6[/tex]

[tex]Area = 13.0695[/tex]

Solving (b): Area when both leaves are up.

Simply multiply the area in (a) by 2

[tex]Area = 2 * 13.0695[/tex]

[tex]Area = 26.139[/tex]

Answer:

Step-by-step explanation:

Combination of 3 teachers out of 12:

Combination of 4 students out of 43:

Total combinations:

Answer:

Step-by-step explanation:

Answer:

That's barely readable!  Anyway the solution is:

7x + 7x +2 +5x +7 = 180 degrees

19x + 9 = 180 degrees

19x = 171 degrees

x = 9

So the angles are:

7x = 63 degrees

7x + 2 = 65

5x + 7 = 52

Double check:

Since ALL 3 triangle sides add up to 180:

63 + 65 + 52 = 180 degrees

Step-by-step explanation:

Answer:

A. 40

Step-by-step explanation:

Answer:

A. 40

Step-by-step explanation:

75 ÷ 1.5 = 50 = original number

80% of 50 = 50 × 0.8 = 40

Answer:

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

95°=6r°+47(being vertically opposite angle)

or,48°=6r

or,48=/6=r°

or,r=8°

1 by 4 ^ 256 is equal to 4 and 1 by 4 ^ 64 will be root 4 so here the answer will be 4 into 4 root 4

there option 4 will be correct

Answer:

m>-7

Step-by-step explanation:

expand

-10m+15-4<81

-10m+11<81

collect like terms

-10m<81-11

-10m<70

m>-7

Answer:

2nd Graph

Step-by-step explanation:

Bases off the graphs, you gave me, I assume your the equation is

[tex]f(x) = - 4(2) {}^{x} [/tex]

The parent equation of this function is

[tex]f(x) = b {}^{x} [/tex]

Let say x=0

Using the rules of exponets, the y value must be 1 so a critical point is

(0,1)

The function is multiplied by -4.

This means the function is stretched in the y direction by 4 and reflected over the x axis. So our new point will be

(0,-4).

The base 2 the function will get compressed by 1/2.

The best graph that represents this is the second graph

Answer:

C. m<c = 140°

Step-by-step explanation:

Let's analyse each of the given options:

A. m<a = 140° is TRUE

Rationale: angle a and 140° are vertical angles. Vertical angles are congruent.

B. m<b = 140° is TRUE.

Rationale: angle a and 140° are alternate interior angles. Alternate interior angles are congruent.

C. m<c = 140° is NOT TRUE.

Rationale: angle c and 140° are same side interior angles. Same side interior angles are supplementary.

D. m<d = 140° is TRUE.

Rationale: angle d and 140° are corresponding angles. Corresponding angles are congruent.

9514 1404 393

Answer:

  x² +y² -6x -16y +48 = 0

Step-by-step explanation:

Given:

Find:

  general form equation for the circle

Solution;

The standard form equation for the circle is ...

  (x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)

  (x -3)² +(y -8)² = 5²

Subtracting 25 and expanding this will give the general form.

  x² -6x +9 +y² -16y +64 -25 = 0

  x² +y² -6x -16y +48 = 0

_____

Additional comment

"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.

9514 1404 393

Answer:

  50.24 cm

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

  s = rθ

  s = (24 cm)(2/3π) = (24 cm)(2/3)(3.14) = 50.24 cm

Answer:

128 mph

Step-by-step explanation:

1 hour = 400

4 hours = 240

240+400= 640

4+1 = 5

640/5=128

Answer:

p = 2 ; q = 4

Step-by-step explanation:

Given tbe equation :

3p + 2q = 14 - - - (1)

10p + 6q = 44 - - -(2)

What is p and what is q

This is a simultaneous equation ; using elimination method :

Multiply (1) by 6 and (2) by 2

18p + 12q = 84 - - - - (3)

20p + 12q = 88 - - - (4)

Subtract (3) and (4)

-2p = - 4

p = 4/2

p = 2

Put p = 2 in (1)

3p + 2q = 14

3(2) + 2q = 14

6 + 2q = 14

2q = 14 - 6

2q = 8

q = 8/2

q = 4

p = 2 ; q = 4

Answer:

Step-by-step explanation:

[tex]h(t)=-16t^2+96t\\\\h(t)=-t(16t-96)[/tex]

[tex]96=2^5*3\\\\16=2^4\\\\h(t)=-t(2^5*3*t-2^4)=-2^4t(2^1*3*t-1)\\\\h(t)=-16t(6t-1)[/tex]

the b) part is easy do it!

Answer:

13/5a - 8/5

Step-by-step explanation:

= 35/15a + 4/15a - 8/5

= 39/15a - 8/5

= 13/5a - 8/5

The simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.

It is defined as the combination of constants and variables with mathematical operators.

It is given that the expression is,7/3a - 8/5 +4/15a.

We have to simplify the expression.

We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

=7/3a - 8/5 +4/15a

= 35/15a + 4/15a - 8/5

= 39/15a - 8/5

= 13/5a - 8/5

Thus, the simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.

Learn more about the expression here:

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Answer:

Hello friend kya in snap and p to Trisha

Answer:

y = 2x

Step-by-step explanation:

Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,

[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]

Answer:

[tex]<-144e^{0.88},7.47e^{0.88}>[/tex]

Step-by-step explanation:

We are given that

[tex]f(u,v)=n^2e^{\frac{u+n}{v+n}}[/tex]

Point=(3,5)

n=12

We have to find the direction at which he moves down the hills quickly.

[tex]f(u,v)=144e^{\frac{u+12}{v+12}}[/tex]

[tex]f_u(u,v)=144e^{\frac{u+12}{v+12}}[/tex]

[tex]f_u(3,5)=144e^{\frac{3+12}{5+12}}[/tex]

[tex]f_u(3,5)=144e^{\frac{15}{17}}=144e^{0.88}[/tex]

[tex]f_v(u,v)=144e^{\frac{u+12}{v+12}}\times (-\frac{u+12}{(v+12)^2})[/tex]

[tex]f_v(3,5)=144e^{\frac{15}{17}}(-\frac{15}{(17)^2}[/tex]

[tex]f_v(3,5)=-\frac{2160}{289}e^{\frac{15}{17}}=-7.47e^{0.88}[/tex]

[tex]\Delta f(3,5)=<f_u(3,5),f_v(3,5)>[/tex]

[tex]\Delta f(3,5)=<144e^{0.88},-7.47e^{0.88}>[/tex]

The direction at which he moves down the hills quickly=-[tex]\Delta f(3,5)[/tex]

The direction at which he moves down the hills quickly=[tex]<-144e^{0.88},7.47e^{0.88}>[/tex]

Answer:

100

Step-by-step explanation:

I assume you mean [tex]\frac{5}{12}[/tex] of the students in Year 9.

Basically, first you need to work out 1/12 of the students, which is just 240 divided by 12, equals 20.

So, we know 1/12 of 240 is 20, therefore, in order to work out 5/12, we must do 20 x 5, which is 100.

Answer:

[tex]T_n = \frac{1}{4^{n-1}}[/tex]

Step-by-step explanation:

Given

[tex]({)1, 1/4, 1/16, 1/64, 1/256, ... (})[/tex]

Required

The general term

The given sequence is geometric.

So first, we calculate the common ratio (r)

[tex]r = T_2/T_1[/tex]

So, we have:

[tex]r = 1/4 \div 1[/tex]

[tex]r = 1/4[/tex]

The function is then calculated using:

[tex]T_n =T_1 * r^{n-1}[/tex]

This gives

[tex]T_n =1 * 1/4^{n-1}[/tex]

[tex]T_n = \frac{1}{4^{n-1}}[/tex]

Answer:

8 classes

Step-by-step explanation:

Given

[tex]Least = 2403[/tex]

[tex]Highest = 11998[/tex]

[tex]n = 225[/tex]

Required

The number of class

To calculate the number of class, the following must be true

[tex]2^k > n[/tex]

Where k is the number of classes

So, we have:

[tex]2^k > 225[/tex]

Take logarithm of both sides

[tex]\log(2^k) > \log(225)[/tex]

Apply law of logarithm

[tex]k\log(2) > \log(225)[/tex]

Divide both sides by log(2)

[tex]k > \frac{\log(225)}{\log(2)}[/tex]

[tex]k > 7.8[/tex]

Round up to get the least number of classes

[tex]k = 8[/tex]

Answer:

44

Step-by-step explanation:

Let x represent the number.

Create an equation, and solve for x:

4x = 6x - 88

-2x = -88

x = 44

So, the number is 44.

The number is 44.

To find the number.

science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers. Arithmetic is the basics of the abstract science of numbers and operations on them. The formula for any arithmetic sequence is this: an = a1 + d (n - 1).

Given that:

Let x represent the number.

Create an equation, and solve for x:

4x = 6x - 88

-2x = -88

x = 44

So, the number is 44.

Learn more about arithmetic here:

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Answer:

The interval is [98,132]

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal with mean 115 and standard deviation 25.

This means that [tex]\mu = 115, \sigma = 25[/tex]

Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.

Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.

25th percentile:

X when Z has a p-value of 0.25, so X when Z = -0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = -0.675*25[/tex]

[tex]X = 98[/tex]

75th percentile:

X when Z has a p-value of 0.75, so X when Z = 0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = 0.675*25[/tex]

[tex]X = 132[/tex]

The interval is [98,132]

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[tex]{hope it helps}}[/tex]