In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC? ∠BTA ≅ ∠CTA ∠BAT ≅ ∠CAT

Answer:

[tex]{ \bf{formular : \: { \tt{volume = \frac{4}{3} \pi {r}^{3} }}}} \\ { \tt{volume = \frac{4}{3} \times 3.14 \times {( \frac{5}{2}) }^{3} }} \\ { \tt{volume = 65.4 \: cubic \: inches}}[/tex]

Answer:

65

Step-by-step explanation:

formula =   4/3 * 3.14* r^3

               = 4/3 * 3.14 * 2.5^3 (radius is half of the diameter)

                    = 65.44985

                     rounded to 65

Answer:

8.

Step-by-step explanation:

The slope =

difference in y coordinates of 2 points / difference in coordinates of corresponding x coordinates.

So taking the first 2 points:

The slope =  (18-10) / 0 - (-1)

= 8/1

= 8.

This is confirmed by slope between the second and third points

slope = 26-18/ (1-0) = 8.

Answer:

A the answer is A if you look at it .

Answer:

The first one is B) point D

The second one is D) (0,0)

Hope this helps!

btw, coordinates are in (x,y) form, so the other answer above me is wrong.

9514 1404 393

Answer:

  9 : 49

Step-by-step explanation:

Assuming the rectangles are similar, the ratio of their areas is the square of the ratio of their side lengths.

  sides ratio = 3 : 7

  areas ratio = 3² : 7² = 9 : 49

Given that,

The angles in a triangle are represented by x, x+10, and x+50.

We had to,

find the measure of the largest angle.

Let's start to solve,

→ x + (x+10) + (x+50) = 180°

→ x + x + x = 180° (-50 -10)

→ 3x = 180° -60

→ 3x = 120

→ x = 120/3

→ x = 40°

Then the value of x + 10,

→ x + 10

→ 40 + 10

→ 50°

Then the value of x + 50,

→ x + 50

→ 40 + 50

→ 90°

The measure of the largest angle is,

→ D. 90 degrees

Hence, option (D) is correct answer.

Step-by-step explanation:

good of you and good workings

Answer:

The correct answer will be "-1.66".

Step-by-step explanation:

Let z₀ be,

[tex]P(z<z_0)=4.8 \ percent[/tex]

                [tex]=0.048[/tex]

⇒ [tex]\Phi (z_0)=0.048[/tex]

Now,

⇒ [tex]\Phi (-1.6646)=0.048[/tex]

   [tex]z_0=-1.6646[/tex]

       [tex]\simeq -1.66[/tex]

Thus the above is the right answer.

Answer:

x≤9/2

Step-by-step explanation:

8x+15≤51

Subtract 15

8x+15-15≤51-15

8x+≤36

Divide by 8

8x/8≤36/8

x≤9/2

Answer:

1 3 5 7 9 11

Step-by-step explanation:

same like this do the question the answer will come

Step-by-step explanation:

[tex] \frac{ \frac{6}{7} }{ \frac{9}{14} } [/tex]

[tex] = \frac{6}{7} \times \frac{14}{9} [/tex]

[tex] = \frac{2}{1} \times \frac{2}{3} [/tex]

[tex] = \frac{4}{3} = 1 \frac{1}{3} (Ans) [/tex]

[tex] \frac{18}{x} = \frac{6}{10} [/tex]

[By cross multiplication]

=> 18 × 10 = 6 × x

[tex] = > \frac{18 \times 10}{6} = x[/tex]

=> 3 × 10 = x

=> x = 30 (Ans)

Answer:

11.33

Step-by-step explanation:

First find the markup

8.80 * 25%

8.8 *.25 = 2.20

The new price is 8.80+2.20 = 11

Now find the tax

11*.03

.33

Add the tax to the new price

11+.33

11.33

Answer:

$11.33

Step-by-step explanation:

First divide 25% by 100, 0.25.

Then multiply 8.80 x 0.25 = 11.

Again, divide 3% by 100, 0.03

Then finally take 11.00 and multiply it with 0.03.

11.00 x 0.03=

$11.33

Answer:

[tex]5\sqrt{2} \\45[/tex]

Step-by-step explanation:

just multiply

Answer:

a) 5√2

b) 135

Step-by-step explanation:

√5·√10 is equivalent to √50, which in turn is equivalent to √25·√2, or 5√2.

√27·√75 can be simplified by factoring:

√3·√9·√3√25, or (because √3·√3 = 3):

(3)(9)(5) = 135

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

7 + 18 = 25 employees, which means that [tex]N = 25[/tex]

7 over 50, which means that [tex]k = 7[/tex]

10 dismissed, which means that [tex]n = 10[/tex]

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]

0.055 = 5.5% probability that exactly 5 employees were over 50.

Answer:

The 98% confidence interval for the mean number of hours of study time per week for all students is (20.9, 25.1).

Step-by-step explanation:

Confidence interval:

Sample mean plus/minus the margin of error.

In this question:

Mean of 23.

Margin of error 2.1.

Then

23 - 2.1 = 20.9

23 + 2.1 = 25.1

The 98% confidence interval for the mean number of hours of study time per week for all students is (20.9, 25.1).

Answer:

y= -3x +40

Step-by-step explanation:

Properties of perpendicular bisector:

• perpendicular to the given line

• cuts through the center of the given line

The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y -intercept.

Let's find the gradient of the given line first.

[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]

Gradient of given line

[tex] = \frac{6 - 2}{18 - 6} [/tex]

[tex] = \frac{4}{12} [/tex]

[tex] = \frac{1}{3} [/tex]

The product of the gradients of perpendicular lines is -1.

m(⅓)= -1

m= -1(3)

m= -3

Substitute m= -3 into the equation:

y= -3x +c

To find the value of c, substitute a pair of coordinates in which the perpendicular bisector passes through into the equation. Since perpendicular bisectors passes through the center of the segment, we can find the point in which the perpendicular bisector passes through using the mid- point formula.

[tex]\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}[/tex]

Midpoint

[tex] = ( \frac{6 + 18}{2} , \frac{6 + 2}{2} )[/tex]

[tex] = ( \frac{24}{2} , \frac{8}{2} )[/tex]

[tex] = (12,4)[/tex]

y= -3x +c

when x= 12, y= 4,

4= -3(12) +c

4= -36 +c

c= 4 +36

c= 40

Thus, the equation of the perpendicular bisector is y= -3x +40.

Answer:

rectangle- 2 lines of reflection

trapezoid- 0 lines of reflection

regular pentagon- 5 lines of reflection

square- 4 lines of reflection

Step-by-step explanation:

Answer:

[tex]y-3=\frac{3}{4} (x-5)\\\\y-3=\frac{3}{4}x-\frac{3}{4}(5)\\\\y=\frac{3}{4} x+3-\frac{15}{4} \\\\y=\frac{3}{4} x+\frac{12}{4} -\frac{15}{4} \\\\y=\frac{3}{4} x-\frac{3}{4}[/tex]

Is this standard form? :\

Answer:

3x-4y=3

Step-by-step explanation:

Hi there!

We are given the equation y-3=[tex]\frac{3}{4}(x-5)[/tex], and we want to write it in standard form

Standard form is given as ax+by=c, where a, b, and c are integer coefficients, a CANNOT be 0 and CANNOT be negative, and b also CANNOT be 0

So let's expand the parentheses in the equation

Do the distributive property

y-3=[tex]\frac{3}{4}x-\frac{15}{4}[/tex]

Add 3 to both sides

y=[tex]\frac{3}{4}x-\frac{3}{4}[/tex]

We expanded the parentheses, but the equation is now in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

Remember that we want it in standard form, which is ax+by=c

Subtract [tex]\frac{3}{4}x[/tex] from both sides

[tex]\frac{-3}{4}x+y=\frac{-3}{4}[/tex]

Remember that the coefficients of a, b, and c need to be integers, and also that a (the coefficient in front of x) CANNOT be negative

So multiply both sides by -4

[tex]-4(\frac{-3}{4}x+y)=-4(\frac{-3}{4})[/tex]

Distribute -4 to every number

[tex]-4(\frac{-3}{4}x)+-4(y)=-4(\frac{-3}{4})[/tex]

Multiply

[tex]\frac{12}{4}x-4y=\frac{12}{4}[/tex]

Simplify

3x-4y=3

There's the equation in standard form

Hope this helps!

Step-by-step explanation:

here is the ans

the perimeter= 130m

hope so this might help you

Answer:

D

Step-by-step explanation:

The table gives us the squares of certain values, and can be used to find the square root of certain values as well. For example, if 6² = 36, we can say that √36 = 6. Given this information, we can say that √47.6 is 6.9, and √49 = 7. If we look at the square root graph (√x=y), we can see that as x goes up, y goes up, and when x goes down, y goes down.

Therefore, we can say that the square root of 48 is between 6.9 and 7. We don't know exactly where it is, as there is no formula given to find it, so what Gina can do is go through the values between 6.9 and 7.0 and look for √48

Answer:

its 1900 Bc. Because BC stand for before chirst

Step-by-step explanation:

Answer:

C) (-6,0)(2,0)

For x-intercept, f(x) = 0:

[tex]{ \tt{ {x}^{2} + 4x - 12 = 0 }} \\ { \tt{(x - 2)(x + 6) = 0}} [/tex]

Answer:

C) (-6,0)(2,0)

Step-by-step explanation:

f(x)= x²+4x-12

(x-2)(x+6)=0

x=2

x=-6

Answer:

its the first square one that says "6 inch, 5 inch"

Step-by-step explanation:

Because 6+6=12 and 5+5=10, so 12+10=22

Answer:

6 and 5 inch

Step-by-step explanation:

Answer:

97.8

Step-by-step explanation:

add together 97.3 +0.5

Answer:

Maybe

1/8 is the probability that the first two assignments Ms.patel collected were completed in pencil

Answer:

20%

Step-by-step explanation:

3.5 - 2.8 = 0.7

0.7 ÷ 3.5 = 0.2

0.2 × 100 = 20

The answer is 20%.

Hope this helped.

Answer:

predicted wight=2.8

Actual wight = 3.5 pounds

(3.5-2.8)/3.5

=0.7/3.5 × 100

=100/5=20%

Answer: 20%

OAmalOHopeO

Answer:

13

Step-by-step explanation:

Its calculate the common difference first.

(95-11)/(n-1).

We also have the sum of these n terms is 689.

So we have the following:

11

+(11+(95-11)/(n-1))

+(11+2(95-11)/(n-1))

+...

+(11+(n-1)(95-11)/(n-1))

This can be re-expressed alittle:

There are (n) amount of 11's in the addition... also 1+2+3+...+(n-1)=(n-1)(n)/2.

So we have the sum is

11(n)+n(n-1)/2×(95-11)/(n-1)

But this equal to 689.

We need to solve the following equation: ​

11(n)+n(n-1)/2×(95-11)/(n-1)=689

The (n-1)'s in second term can cancel.

11(n)+n/2×84=689

11n+42n=689

53n=689

53n=689

n=689/53

n=13

The number of the terms for the arithmetic series is 13.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

The formula for calculating the sum of the arithmetic progression.

Sn = ( n / 2 ) [ a₁ + a[tex]_{n}[/tex]]

689 = ( n / 2 ) [ 11 + 95 ]

689 x 2 = n x 106

n = 1378 / 106

n = 13

Therefore, the number of terms for the arithmetic series is 13.

To know more about arithmetic progression follow

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Answer:

i think its 2 1

Step-by-step explanation:

Answer:

y =2/3x-1

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

   = ( 3-1)/ (6-3)

   = 2/3

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 2/3x +b

Using a point

3 = 2/3(6)+b

3 = 4+b

3-4 =b

-1=b

y =2/3x-1

Answer:

Mix fraction: 3 1/27

Improper fraction: 82/27

Decimal approximation: 3.037

Step-by-step explanation:

What value is close to 28 that is a perfect cube...27 which equals 3^3.

So let's find the tangent line to the curve y=cubert(x) at x=27.

We will use this equation to approximate what happens at x=28.

First let's rewrite the radical in our equation;

y=x^(1/3)

Now differentiate

y'=(1/3) x^(1/3-1) by power rule

Simplify

y'=(1/3) x^(-2/3) or (1)/(3x^[2/3])

So the slope of our tangent line at x=27 is (1)/(3(27)^[2/3])=1/(3(3)^2)=1/(3×9)=1/27.

We will also need a point on this tangent line....We know we have the point at x=27 because that is what our tangent line to curve is being found at.

So at x=27, we have y=cubert(27)=3. We used our equation y=cubert(x) here.

So we want to find the equation of the line that contains point (27,3) and has slope 1/27.

Point-slope form is

y-y1=m(x-x1)

Plug in our values

y-3=(1/27)(x-27)

Add 3 on both sides

y=3+(1/27)(x-27)

We will use this linear equation to approximate cubert(28) by replacing x with 28.

y=3+(1/27)(28-27)

y=3+(1/27)(1)

y=3+1/27

You can write that as a mix fraction if you want.

This value is than 3 but super close to 3 since 1/27 is close to 0.

Mix fraction: 3 1/27

Improper fraction: 82/27

Decimal approximation: 3.037

Cubert of 28 when smashed into calculator as is gives approximately 3.0366 which is pretty close to our approximation.

Using a linear approximation method  f'(29)  ≈ 3.1465.

A linear approximation is an approximation of a general function using a linear function (specifically, an affine function). They are widely used in the finite difference method to establish first-order methods to solve or approximate the solutions of  equations.

Linear approximation, or linearization, is a method by which we can  approximate the value of a function at a certain point. The reason linear approximation is useful is that finding the value of a function at a particular point can be difficult. Square roots are a good example of this.

Linear approximated as:

f(x+Δx)≈f (x)+Δx x[tex]f^{'}[/tex](x)

Take x = 28 and Δx = 1

f(x) = [tex]\sqrt[3]{x}[/tex]

Substitute 28for x

f(x) = [tex]\sqrt[3]{28}[/tex]

f(x) = 3.0365

So, we have

f(x+Δx)≈f (x)+Δx x[tex]f^{'}[/tex](x)

f(28+1)≈3.0365+1.[tex]f^{'}[/tex](x)

f(29)≈3.0365+1.[tex]f^{'}[/tex](x)

To calculate f'(x)

We have

f(x)=[tex]\sqrt[3]{x}[/tex]

Rewrite as

f(x)= [tex]x^{\frac{1}{3} }[/tex]

Differentiate

[tex]f^{'}[/tex]= [tex]\frac{1}{3}[/tex][tex]X^{\frac{1}{3}-1 }[/tex]

f' = [tex]\frac{1}{3}[/tex] . [tex]\frac{x^{\frac{1}{3} } }{3x}[/tex]

f'(29) = [tex]\frac{29^{\frac{1}{3} } }{3\times29}[/tex]

f'(29) =9.66/87

f'(29)  = 3.22/29

f'(29)  ≈ 3.0365+1x 3.22/29

f'(29)  ≈3.0365+ 0.1110

f'(29)  ≈ 3.1465

To learn more about differential  equation, refer;

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Answer:

33 years

Step-by-step explanation:

Given the quadratic model :

P=0.006A2−0.02A+120

P = blood pressure ; A = Age

Given a blood pressure value of 126 mmHg ; the age, A will be ;

The equation becomes :

126 = 0.006A2−0.02A+120

0.006A² - 0.02A + 120 - 126 = 0

0.006A² - 0.02A - 6 = 0

Using the quadratic formula :

-b ± (√b²-4ac) / 2a

a = 0.006 ; b = - 0.02 ; c = - 6

Using calculator :

The roots are :

a = 33.333 or a = - 30

Age cannot be negative, hence, the age, A will be 33.333

Total the nearest year ; Age = 33 years