Eight less than four times a number is less than 56. What are the possible values of that number?
X> 12
x < 12
ООО
x < 16
O x> 16

Answers

Answer 1

Answer:

x < 16

Step-by-step explanation:

Let the number be x

Four time the number = 4x

Eight less than four times the number = 4x - 8

Eight less than four times the number is less than 56,

          that is , 4x - 8  < 56

                      4x - 8 + 8 < 56 + 8                    [ adding both sides by 8 ]

                        4x + 0 < 64

                              4x < 64                             [ divide both sides by 4 ]

                                 x < 16

                         


Related Questions

Sam wants to build a unique pyramid bookend for his study. It's an oblique pyramid
with a right triangular base. The sides of the base are 3, 4, and 5 inches long. The
pyramid will fit exactly inside his bookshelf, which has a height of 18 inches. He
wishes to build the pyramid out of modeling clay. How many cubic inches of clay
does Sam need to buy?

36in^3
24in^3
62.8in^3
216in^3

Answers

Answer:

Volume of triangular pyramid = 36 inch³

Step-by-step explanation:

Given:

Sides of base triangle = 3, 4, 5 inches

Height of model = 18 inches

Find:

Volume of triangular pyramid

Computation:

Given base triangle is a right angle triangle

So,

Area of base = (1/2)(b)(h)

Area of base = (1/2)(3)(4)

Area of base = (1/2))(12)

Area of base = 6 inch²

Volume of triangular pyramid = (1/3)(Area of base)(Height of model)

Volume of triangular pyramid = (1/3)(6)(18)

Volume of triangular pyramid = 36 inch³

What is the product (4.42 x 103)(5 x 10^) written in
scientific notation?

Answers

Answer:

2.2763 x 10 to the power of 4

for some reason it doesn't let me put in the explanation

The force F (in pounds) needed on a wrench handle to loosen a certain bolt varies inversely with the length L (in inches) of the handle. A force of 40 pounds is needed when the handle is 7 inches long. If a person needs 20 pounds of force to loosen the bolt, estimate the length of the wrench handle. Round answer to two decimal places if necessary.
in inches

Answers

Answer:

14 inches

Step-by-step explanation:

Since F is inversely proportional to L,

[tex]f = \frac{k}{l} \\ when \: f = 40 \: l \: = 7 \\ \frac{k}{7} = 40 \\ k = 280 \\ when \: f = 20 \\ 20 = \frac{280}{l} \\ l = 14[/tex]

How many x-intercepts are in the quadratic equation y = 7x2 − 2x − 1​

Answers

Answer:

There are 2 x intercepts

What is the answer
5 10 25 100 × ÷ ÷

Answers

Answer: 1/50, or 0.02

Step-by-step explanation:

I'm assuming this is 5*10/25/100. if you just follow the equation, you get 50/25/100, which is 2/100, or 1/50.

Simplify
b. 3a + 4b-2a-b
4 나
V
216 x
Х
18

Answers

Answer:

a+3b

Step-by-step explanation:

3a+4b-2a-b

=3a-2a+4b-b

=a+3b

In any triangle ABC,Prove by vector method c^2=a^2+b^2-2abcosC​

Answers

Answer:

Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:

[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]

[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]

[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]

[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]

[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]

Step-by-step explanation:

Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:

[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]

[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]

[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]

[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]

[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]

Which figure can be formed from the net?
pls answer fast for brainiest !

Answers

Answer:

It should be the top right one

(with 6ft as the height)

Step-by-step explanation:

Answer:

It must be the lower to the left choice.

Step-by-step explanation:

As you can see, the net we have is composed of only triangles.

So we should be choosing a figure with a triangular base.

Our answers are narrowed down into the top right and lower left choices because both figures have triangular bases.

The other person down there chose the top right choice and was incorrect, so the answer should be the lower to the left figure.

Also, its the lower left figure because look at the triangular base, it is an isosceles meaning that two sides have the same length.

If the net says that the long side measures 9 ft, then the other two sides should be the same length and shorter than 9 ft. So the answer is the lower left figure.

Hope this helps

Solve the simultaneous equations
6
x
+
2
y
=
12
5
x
+
2
y
=
8

Answers

Answer: x=4, y=-6

Step-by-step explanation:

With a.b.c=1 and a+b+c=1
Prove that:

Answers

Answer:

HOPE IT HELPS PLZ MARK ME BRAINLIEST

Step-by-step explanation:

abc=1

⟹c=1/ab

1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a)

=1/(1+a+1/b)+1/(1+b+ab)+1/(1+1/ab+1/a)

=b/(1+b+ab)+1/(1+b+ab)+ab/(1+b+ab)

=1+b+ab/(1+b+ab)

=1

In 1999, a company had a profit of $173,000. In 2005, the profit was
$206,000. If the profit increased by the same amount each year, find the
rate of change of the company's profit in dollars per year. *
$5,500
$4,004
$379,000
$33,000
O $102.74

Answers

Answer:

A. $5500

Step-by-step explanation:

The difference of years:

2005 - 1999 = 6

The difference in profit over 6 years:

206000 - 173000 = 33000

Average rate of change:

33000/6 = 5500

It has been 6 years,

The main difference in profit over 6 years between 1999 and 2005 is,

→ 206000 - 173000

→ 33000

Then the average rate of change is,

→ 33000/6

→ 5500

Hence, $ 5500 is the correct option.

Hi I need help with fraction
1
_ x 10
8.

Answers

Answer:

The answer is 1 1/4 or 5/4

Step-by-step explanation:

1/8 · 10 = 10/8

10/8 when simplified is 5/4

the answer is 5/4 simplified

use the figure below to find the answer. find y.

Answers

9514 1404 393

Answer:

  y = 7√2

Step-by-step explanation:

We are given the side opposite the angle, and we want to find the hypotenuse. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(45°) = 7/y

  y = 7/sin(45°) = 7/(1/√2)

  y = 7√2

__

Additional comment

In this 45°-45°-90° "special" right triangle, the two legs are the same length. Thus, ...

  x = 7

In rural Ireland, a century ago, the students had to form a line. The student at the front of the line would be asked to spell a word. If he spelled it correctly, he was allowed to sit down. If not, he received a whack on the hand with a switch and was sent to the end of the line. Suppose the student could spell correctly 60% of the words in the lesson. What is the probability that the student would be able to sit down before receiving four whacks in the hand?

Answers

Answer:

The answer is "0.9102"

Step-by-step explanation:

P(student spell correct) = 0.6

P(student spell incorrect)=1-0.6=0.4

X=the pupil will be allowed to sit down after receiving three slaps on the hand Thus, X would assume Value

X=0 (student sit sans getting whacks)

X=1 (student sit down without receiving 1 whack) (student sit down without receiving 1 whack)

X=2 (student take a seat before receiving 2 whacks)

X=3 (student sit down after receiving 3 punches)

[tex]\to P(X)=0.6 \times 0.4^0 +0.6 \times 0.4 + 0.6 \times 0.4 ^2 + 0.6 \times 0.3^3[/tex]

             [tex]=0.6 \times 1+0.24 + 0.6 \times 0.09 + 0.6 \times 0.027\\\\=0.6 +0.24 + 0.054 + 0.0162\\\\=0.9102\\\\[/tex]

A school band found they could arrange themselves in rows of 6, 7, or 8 with no one left over. What is the minimum number of students in the band?

Answers

Answer:

168 is the answer if i m not wrong.I took the LCM.

If school band found they could arrange themselves in rows of 6, 7, or 8 with no one left over, the minimum number of students in the band is 168.

To find the minimum number of students in the band, we need to determine the least common multiple (LCM) of the numbers 6, 7, and 8.

The LCM is the smallest multiple that is divisible by all the given numbers.

Prime factorizing each number, we have:

6 = 2 * 3

7 = 7

8 = 2 * 2 * 2

To find the LCM, we take the highest exponent for each prime factor:

2³ * 3 * 7 = 168

By having 168 students, they can arrange themselves into rows of 6 (28 rows), 7 (24 rows), or 8 (21 rows) without anyone being left over. Any fewer than 168 students would result in at least one row having students left over.

To learn more about LCM click on,

https://brainly.com/question/1771764

#SPJ2

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y -4 = %(x -8). What is
the slope-intercept form of the equation for this line?
O y = ÷x-12
O y= x-4
O y= =x+2
O y= =x +6

Answers

Answer:

y= x-4

Step-by-step explanation:

find 9 rational no. between 8/7 and 17/10.​

Answers

Answer:

[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]

Step-by-step explanation:

We need to find 9 rational number between [tex]\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}[/tex]

We make the denominators of both fractions same. So,

[tex]\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}[/tex]

and

[tex]\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}[/tex]

The rational number are:

[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]

A real estate agent has 12 properties that she shows. She feels that there is a 30% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling no more than 2 properties in one week. Round your answer to four decimal places.

Answers

Answer:

0.2528 = 25.28% probability of selling no more than 2 properties in one week.

Step-by-step explanation:

For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

A real estate agent has 12 properties that she shows.

This means that [tex]n = 12[/tex]

She feels that there is a 30% chance of selling any one property during a week.

This means that [tex]p = 0.3[/tex]

Compute the probability of selling no more than 2 properties in one week.

2 or less sold, which is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{12,0}.(0.3)^{0}.(0.7)^{12} = 0.0138[/tex]

[tex]P(X = 1) = C_{12,1}.(0.3)^{1}.(0.7)^{11} = 0.0712[/tex]

[tex]P(X = 2) = C_{12,2}.(0.3)^{2}.(0.7)^{10} = 0.1678[/tex]

Then

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0138 + 0.0712 + 0.1678 = 0.2528[/tex]

0.2528 = 25.28% probability of selling no more than 2 properties in one week.

At a snack food manufacturing facility, the quality control engineer must ensure that all products feature the appropriate expiration date. Suppose that a box of 60 candy bars includes 12 which do not have the proper printed expiration date. The quality control engineer, in inspecting the box, grabs a handful of seven candy bars. What is the probability that there are exactly 3 faulty candy bars among the seven

Answers

Answer:

0.1108 = 11.08% probability that there are exactly 3 faulty candy bars among the seven.

Step-by-step explanation:

The bars are chosen 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:

60 total candies means that [tex]N = 70[/tex]

12 are faulty, which means that [tex]k = 12[/tex]

Seven are chosen, so [tex]n = 7[/tex]

What is the probability that there are exactly 3 faulty candy bars among the seven?

This is [tex]P(X = 3)[/tex]. 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 = 3) = h(3,70,7,12) = \frac{C_{12,3}*C_{48,4}}{C_{60,7}} = 0.1108[/tex]

0.1108 = 11.08% probability that there are exactly 3 faulty candy bars among the seven.

What is the common ratio of the sequence? -2, 6, -18, 54,...
a.-3
b.-2
c.3
d.8

Answers

Answer:

a. -3

Step-by-step explanation:

-2 turns into 6 by multiplying it by -3.

the same from 6 to -18, from -18 to 54, ...

so, an/an+1 = -3

identify the largest value in fraction 3/4, 1/2, 3/5

Answers

Answer:

1/2

Step-by-step explanation:

The largest value in fraction it is 1/2 because the fraction is small amount .while the 3/4 is least amount .and 3/5 is greatest amount fractions

Find the domain and range of the relation.

Answers

the answer is in the picture above

What is the correct definition for sec theta?

Answers

Answer:

D Is the correct answer Thats was too easy

Answer:

sec(θ) = hypotenuse / adjacent.

Step-by-step explanation:

sec theta= cos -1  theta

If 19,200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Answers

Step-by-step explanation:

√19200cm²

=138.56cm

then the highest possible volume

=(138.56)³

=2660195.926cm³

The largest possible volume of the box is; V = 25600 cm³

Let us denote the following of the square box;

Length = x

Width = y

height = h

Formula for volume of a box is;

V = length * width * height

Thus; V = xyh

but we are dealing with a square box and as such, the base sides are all equal and so; x = y. Thus;

V = x²h

The box has an open top and as such, the surface are of the box is;

S = x² + 4xh

We are given S = 19200 cm². Thus;

19200 = x² + 4xh

h = (19200 - x²)/4x

Put (19200 - x²)/4x for h in volume equation to get;

V = x²(19200 - x²)/4x

V = 4800x - 0.25x³

To get largest possible volume, it will be dimensions when dV/dx = 0. Thus;

dV/dx = 4800 - 0.75x²

At dV/dx = 0, we have;

4800 - 0.75x² = 0

0.75x² = 4800

x² = 4800/0.75

x² = 6400

x = √6400

x = 80 cm

From h = (19200 - x²)/4x;

h = (19200 - 80²)/(4 × 80)

h = (19200 - 6400)/3200

h = 4 cm

Largest possible volume = 80² × 4

Largest possible volume = 25600 cm³

Read more at; https://brainly.com/question/19053087

What can you say about the y-values of the two functions f(x) = 3x -3 and
g(x) = 7x2 -3?

Answers

9514 1404 393

Answer:

the y-values of g(x) are limited to values of at least -3, those of f(x) are not limitedthe y-values are the same for two different x-values

Step-by-step explanation:

You can say lots of things about the y-values of these functions. A couple of observations are listed above. In addition, we can say the y-values of g(x) will be greater than those of f(x) for x-values not equal or between the x-values where the y-values are the same.

Answer:

• g(x) has the smallest possible y-value.

• The minimum y value of g(x) is -3.

Step-by-step explanation:

Ap3x

1 cm = 5km scale ratio

Answers

Answer: Definition: Ratio of the size of the map to its subject: Scale ... so scale = 1 cm / 100,000 cm = 1/100,000. - Scale ... STEP 1: - 2 cm represents 5 km

Step-by-step explanation:

STEP 1: - 2 cm represents 5 km - (write in full)

- STEP 2: - 1 cm represents 2.5 km - (divide so left side = 1)

- STEP 3: - 1 cm represents 250,000 cm - (convert to same units)

- STEP 4: - scale is 1 : 250,000 - (express as a representative fraction)

Read the following scenario, and then answer the question.

Juan assumes that the temperature of the hot tea cooling on his desk can be modeled with an exponential function like this one: T(t)=179(0.92)t. He bases his assumption on the following: The tea cools about 8% every minute. The tea's current temperature is around 179 degrees Fahrenheit.

Which explanation correctly addresses Juan's assumption?

He is incorrect. The tea will cool linearly since it cools at the same number of degrees every minute.
He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.
He is incorrect. The tea will cool along the curve of a parabola since it cools at an increasing percentage rate every minute.

Answers

9514 1404 393

Answer:

  (b)  He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.

Step-by-step explanation:

Newton's Law of Cooling says the change in temperature is proportional to the temperature. This relation gives rise to an exponential function describing the temperature.

In this description, the temperature referred to is the difference between the temperature of the object and the temperature of the environment to/from which heat is being transferred.

Juan is only partially correct. The function is exponential, but the temperature that should be used in his equation is not the temperature of the tea, but the temperature difference between the tea and his desk.

__

The curve is not linear and not parabolic, excluding the other answer choices.

Consider a relation on the set of all states in the United States given by: two states are related if they have a border in common. Is it an equivalence relation

Answers

Answer:

Yes it is an equivalence relation

Explanation:

An equivalence relation is a binary relation between two values that are symmetric, transitive and reflexive. In other words, when we say a value x is equal(using "=") to a value y, there is an equivalence relation between them.

Example, given set {x, y, z} where ~ means equivalence:

x ~ y if y ~ z means symmetric

since x ~ y and y ~ z, then x ~ z means transitive

x ~ x means reflexive

Equivalence relations share a common attribute or attributes(example, a satisfying condition)

The above condition that two states are related from the set of all US states if they have a border in common satisfies the condition of equivalence listed hence it is an equivalence relation.

Please I need help!!!!!!!!

Answers

Answer:

10 is the correct answer

Answer:

Go with the third option 10!

i hope this helped!

Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course depends on the frequency, duration, and type of use. One study involving heavy use of the phones showed the mean of the battery life to be 15.25 hours with a standard deviation of 2.2 hours. Then the battery needs to be recharged. Assume the battery life between charges is normally distributed.

Required:
a. Find the probability that with heavy use, the battery life exceeds 11 hours.
b. You are planning your recharging schedule so that the probability your phone will die is no more than 5%. After how many hours should you plan to recharge your phone?

Answers

Answer:

a) The probability that with heavy use, the battery life exceeds 11 hours is 0.4602.

b) Using the standard normal table, After 6.8 hours should you plan to recharge your phone.

Step-by-step explanation:

a) The probability that with heavy use, the battery life exceeds 11 hours:-

P(x > 11) = 1 - p( x< 11)  

[tex]=1- p P[(x - \mu) / \sigma < (11 - 10.75) / 2.4]\\\\=1- P(z < 0.10)[/tex]  

Using z table distribution,    

= 1 - 0.5398  

= 0.4602  

b) Using the standard normal table,  

[tex]P(Z < z) = 5%\\\\\\\\= P(Z < -1.645 ) = 0.05 \\z = -1.645[/tex]

Using the z-score formula,  

[tex]x = z \times \sigma + \mu\\x = -1.645 * 2.4 + 10.75\\x = 6.8 hours.[/tex]

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