Determine whether the following statement is true or false. If false, give a counterexample. If true, give an argument to support your conclusion.
If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.

Answer:

4/31

Step-by-step explanation:

reciprocal=same thing upside- down,

The scalar multiplication [tex]k(\overrightarrow{a}+\overrightarrow{b})=k\overrightarrow{a}+k\overrightarrow{b}[/tex]has been proved.

Scalar Multiplication Property:

Basically a scalar means the real number.

The scalar multiplication property states that the product of a sum or difference of a number is equal to the sum or difference of the products.

The general form of scalar multiplication as follows:

k (A + B) = kA + k B

where

k is the scalar.

Given,

Let

[tex]\overrightarrow{a}= < x_1,y_1 >[/tex]

and

[tex]\overrightarrow{b}= < x_2,y_2 >[/tex]

Then we have to prove the following scalar multiplication property,

[tex]k(\overrightarrow{a}+\overrightarrow{b})=k\overrightarrow{a}+k\overrightarrow{b}[/tex]

We know that,

"The vector is an object that has both a magnitude and a direction. And  vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction."

Here we have two vectors like [tex]\overrightarrow{a},\overrightarrow{b}[/tex].

Now we need to use the definition of the scalar multiplication property,

Then, the LHS of the expression is written as,

[tex]\implies k(\overrightarrow{a}+\overrightarrow{b})[/tex]

Apply the values of the vectors then we get,

=> k(<x₁, y₁> + <x₂, y₂>)

When we expand the terms then we get,

=> k<x₁, y₁> +  k<x₂, y₂>

And it can be written as,

[tex]\implies k\overrightarrow{a}+k\overrightarrow{b}[/tex]

Therefore, the scalar multiplication property has been proved.

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Answer:(x+3)(x-5)

Step-by-step explanation:(x^2-5x)+(3x-15)

x(x-5)+3(x-5)

(x+3)(x-5)

   From the list of numbers presented we can determine that this is a finite sequence.

 A sequence is defined by an order of values and/or elements that have a relationship of variation as a ratio or proportion that makes them predictable.

  A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:

2.3 + 4.6 + 9.2 +18.4

   We can clearly notice that we have a larger limit number and it is 18.4, as we know the beginning of the sequence and the exact end we can know that we are in the presence of a finite sequence.

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The two terms of each arithmetic sequence [tex]a_{4}[/tex] = 8 [tex]a_{7}[/tex] = 20 are d = 4 and a = -4.

[tex]a_{4}[/tex] = 8

8 = a +3d.............1

[tex]a_{7}[/tex] = 20

20 = a + 6d...........2

equating equation 1 and 2

8 = a +3d

20 = a + 6d

d = 12/3

d = 4...............3

from equation 3

8 = a + 12

a = -4

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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answer:

x=0 or x=4.732050807568877 or x=1.2679491924311228

Using the normal distribution, it is found that:

b)

The maximum 39.5% obese has a z-score of 2.11, hence it is 2.11 standard deviations above the mean.

The minimum 23% obese has a z-score of -2.21, hence it is 2.21 standard deviations below the mean.

c) The interval is 23.79% to 39.07%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

For this problem, the parameters are given as follows:

[tex]\mu = 31.43, \sigma = 3.82[/tex]

The maximum weight is of 39.5, hence:

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

Z = (39.5 - 31.43)/3.82

Z = 2.11.

The maximum 39.5% obese has a z-score of 2.11, hence it is 2.11 standard deviations above the mean.

The maximum weight is of 23, hence:

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

Z = (23 - 31.43)/3.82

Z = -2.21

The minimum 23% obese has a z-score of -2.21, hence it is 2.21 standard deviations below the mean.

For item c, we consider the Empirical Rule, which states that 95% of the measures are within 2 standard deviations of the mean.

Then:

The interval is 23.79% to 39.07%.

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Answer:

Calm down, I gotcha!

Step-by-step explanation:

4 7/12+ 2 3/4+ 7 5/12=14.75

Answer:

first remove the brackets

then find the like terms

and work out

The sampling technique Greg used is stratified sampling.

Stratified sampling is used when the population is more heterogeneous. Then we divide the population into subgroups or strata which will be more homogeneous and take samples from each strata. This will ensure the equal representation from each group in population. Stratified sampling helps to reduce the variability of the estimates also.

Here the population of current season ticket holders consist both for men's basketball games and women's basketball games. So Greg considered both as separate subgroups of the population and collected random samples of size 100 from each group. This technique for sampling is known as stratified sampling.

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Considering the definition of an equation and the way to solve it, the money earned by Adriano's online business this month is $1,150.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

In this case, you know that every month, Adriano receives a subscription fee of $5 from each of the subscribers to his website. Then, the amount of money earned by Adriano's online business each month will be represented by the following equation:

Money earned by Adriano's online business each month= $5x

where x is the number of subscribers on the website.

On the other hand, you know:

Then, the number of subscribers this month can be calculated as:

Number of subscribers this month = 200 + 40 - 10

Number of subscribers this month = 230

So, the amount of money earned by Adriano's online business this month is calculated by substituting this value in the equation above:

Money earned by Adriano's online business this month= $5×230 subscribers

Money earned by Adriano's online business this month=$1,150

Finally, the money earned by Adriano's online business this month is $1,150.

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Answer:

[tex]2\sqrt{x}[/tex]

Step-by-step explanation:

[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}[/tex]

[tex]2x \cdot x^{-\frac{1}{2}} = 2x^{1-\frac{1}{2}} = 2x^{\frac{1}{2}} = 2\sqrt{x}[/tex]

Another way of doing this is to see that
[tex]x^{-\frac{1}{2}} = \frac{1}{\sqrt{x} }[/tex]

So [tex]2x \cdot x^{-\frac{1}{2}} = \frac{2x}{\sqrt{x} } =2\sqrt{x}[/tex]

A cell phone tower is 173.21 feet high.

Consider the following diagram

Let AB be the height of tower, C be the position of Jen.

Jen walks 50 feet from the tower, and finds the angle of elevation from her position to the top of the tower to be 60°

An angle ACB be an angle of elevation.

⇒ ∠ACB = 60°

And AC = 50 ft

We need to find the distance AB.

Consider tangent of angle ACB.

⇒ tan(60) = AB / BC

⇒ 1.7321 = AB / 100

⇒ AB = 1.7321 × 100

⇒ AB = 173.2 feet

Therefore, a cell phone tower is 173.21 feet high.

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Answer:

121° and 59°

Step-by-step explanation:

We'll assign the two angles 'a' and 'b'. Since they are supplementary, this means they add to 180°. We can model this peoblem with the expressions:

a + b = 180° and a - b = 62°

Let's use the second equation to find a substitution for a:

a - b = 62°

a = 62° + b

Now substitute this in the first equation and solve:

(62° + b) + b = 180°

62° + 2b = 180°

2b = 118°

b = 59°

59° + 62° = 121° this is angle a

Answer:

The graph on the screen is

Step-by-step explanation:

Good luck with your studies!

The equation of line in slope intercept form which passes through (-1, -5) and (4, -2) will be y = [tex]\frac{3}{5}[/tex] x .

What is the slope intercept form of a line ?

The equation of a straight line in the form y = mx + c is known as the slope intercept form, where m denotes the slope and c denotes the y-intercept of a line.

It is given that line is passing through (x1 , y1) and (x2 , y2) that is ,  (-1, -5) and (4, -2).

Let's find out the value of slope first.

We know that , slope (m) = (y2-y1) / (x2-x1)

⇒ m = [(-2-(-5)] / [4 - (-1)]

⇒ m = 3 / 5

Now we will use the slope to find the y-intercept.

∵ y = mx + c

where , c is the y-intercept.

(-2 -(-5)) = (3/5) × (4-(-1)) + c

3 = [ (3/5) × 5 ] + c

3 = 3 + c

c = 0

Now ; we will write the equation in slope intercept form that is ;

y = mx + c

or

y = [tex]\frac{3}{5}[/tex] × x + 0

or

y = [tex]\frac{3}{5}[/tex] x

Therefore , the equation of line in slope intercept form which passes through (-1, -5) and (4, -2) will be y = [tex]\frac{3}{5}[/tex] x .

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Answer:

10 tents

Step-by-step explanation:

I don't know if Chetis a person name or not but if it a person name then 76÷8=9.5 because 75+1=76 (including him)

if Chetis is not a person name then 75÷8=9.375

The answer would still be the same which is 10 tents needed.

Answer:

$0.15 per ounce

Step-by-step explanation:

Take the total price and divide by the ounces to get the price per ounce. 3.60/24 equals 0.15

Based on the calculations below, the amount of tuition per year is $36,000 while the amount of the increase in tuition each year is $1,000.

Note: There are two questions in this question as follows:

1. How much is tuition per year?

2. By how much will tuition increase each year?

We can calculate the tuition per year and the increase in the tuition each year as below:

Number of semesters in a year = 2

Tuition in each semester = $18,000

Increase in the tuition per semester = $500

Using the above information, we can proceed as follows:

Tuition per year = Tuition in each semester * Number of semesters in a year = $18,000 = $36,000

Increase in the tuition each year =  Increase in the tuition per semester * Number of semesters in a year = $500 * 2 = $1,000

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Answer: $4490

Step-by-step explanation:

30×48=1440

 1440+(50×61)

1/3 is the  probability when You roll a die and get a 2. You roll another die and get a 3.

In statistics, what does a probability mean?

when a dice is thrown we get the following out comes

S = { 1,2,3,4,5,6}

n(S) = 6

probability of getting 3 is 1/6 [as there is only one 3]

probability of getting 4 is 1/6 [ there is only one 4]

Using addition theorem of of probability ,

probability of getting 3 or 4 is 1/6 + 1/6 = 2/6 = 1/3

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Answer:

8,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Step-by-step explanation:

8(10^42)

Parenthesis is the multipication sign  btw

Answer:

61

Step-by-step explanation:

5•5+36

(5)(5)+36

=25+36

=61

The inverse function as g⁻¹ (h)  = [(h+6)/10]² which is the correct answer would be an option (E).

The inverse function is defined as a function obtained by reversing the given function.

To determine the inverse of a function, all you have to do is switch where h and g are and resolve for g.

So after switching h and g,

g = g(h) = 10√h - 6

becomes

h = 10√g - 6

Now, we solve for h regularly.

h + 6 = 10√g

(h + 6)/10 = √g

[(h+6)/10]² ⇒ g = [(h+6)/10]² = g(x)

Therefore the inverse of g(x) is g⁻¹ (h)  = [(h+6)/10]²

Hence, the inverse function as g⁻¹ (h)  = [(h+6)/10]²

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Common ratio= 1/2, Next two term= 1/16, 1/32

This is a geometric sequence since there is a common ratio between each term.

i.e.,

the common ratio (r) = [tex]\frac{1/2}{1}[/tex] = [tex]\frac{1/4}{1/2}[/tex]

                                  = 1/2

We can write the formula for general term of the series as

[tex]a_{n}[/tex] = a[tex](\frac{1}{2})^{n-1}[/tex]

If the further sequence does continue in the same way then the whole infinite sequence indicated is a geometric series.

So we have

[tex]a_{2}[/tex] =(1) [tex](\frac{1}{2} )^{2-1}[/tex]= 1/2

[tex]a_{3}[/tex] = 1× [tex](\frac{1}{2} )^{3-1}[/tex]= 1/4

[tex]a_{4}[/tex] = 1× [tex](\frac{1}{2} )^{4-1}[/tex]= 1/8

[tex]a_{5}[/tex] = 1× [tex](\frac{1}{2} )^{5-1}[/tex]= 1/16

[tex]a_{6}[/tex] = 1× [tex](\frac{1}{2} )^{6-1}[/tex]= 1/32

......

Therefore the sequence is in the same series, and we get the next two terms of the sequence which are 1/16, 1/32

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The total change in temperature, in degrees Fahrenheit, for the package of food is 50°F

The initial temperature of the package of food as given in the question is -15°F

At noon, the temperature of the package of food was changed to 35° F

We need to find out the total change in temperature which is

Temperature of food package at noon - The initial temperature of the package of food

By substituting the values given in question we get

                       = 35° - (-15° F)

Which is a simple integer problem

                      = 35 - (-15)

                     = 35 + 15

                     =   50 F

Hence, the total change in temperature, in degrees Fahrenheit, for the package of food is 50° F

An integer is the range 0, a wonderful natural number or a poor integer with a minus signal. The poor numbers are the additive inverses of the corresponding advantageous numbers. in the language of arithmetic,

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Answer:

A right triangle

Step-by-step explanation:

The angle of 90 degrees is a right angle

volume of the largest sample is 7 times the volume of the smallest sample.

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.

given:

The volume of the largest sample is 7/8 gallon.

The volume of smallest sample is is 1/8 gallon.

So,

volume of the largest sample/volume of the smallest sample

=7/8 / 1/8

=7/8 * 8/1

=7

Hence, volume of the largest sample is 7 times the volume of the smallest sample.

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ABCD ∽ EFGH, meaning both quadrilaterals are similar, therefore the proportionos of their corresponding sides are equal, thus

[tex]\cfrac{AB}{EF}~~ = ~~\cfrac{CD}{HG}\implies \cfrac{\stackrel{AB}{3}}{\underset{EF}{2}}~~ = ~~\cfrac{\stackrel{CD}{4.5}}{\underset{HG}{y}}\implies 3y=9\implies y=\cfrac{9}{3}\implies y=3[/tex]

Answer:

7 - y

Step-by-step explanation:

The sum of -7 and y: -7 + y

The opposite of the sum: -(-7 + y) = 7 - y