Find z within the problem.

Equivalent expressions, by definition, have the same value but they look different.

In this case:

1. "Less than" indicates a subtraction.

2. "More" indicates addition.

3. "Times" indicates multiplication.

Let be "x" the number.

With the information given, you can write the following equation:

To know the number you must solve for the variable "x":

Therefore, the number is:

Given:

To find:

Solutions

Explanation:

From equation (1),

Substituting equation (3) in (2) we get,

Therefore, the system has infinitely many solutions.

Final answer:

INFINITELY MANY

Answer:

19 would be the naswer

Step-by-step explanation:

Answer: 8/11

Step-by-step explanation:

To find slope you can use this formula:

y2-y1/x2-x1

substitute the values with the ones from the 2 points

-13-(-5)= -8

-19-(-8)=-11

you then divide -8/-11

and you get 8/11

8/11 is the slope of those 2 points.

The Nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.

To determine the time the flag is in the air before Zack catches it, we can use the kinematic equation for vertical motion:

h = 16t^2 + vt + s

Where:

h is the height of the flag,

t is the time in seconds,

v is the initial vertical velocity of the flag,

s is the initial height of the flag.

In this case, the flag is thrown into the air from a height of 5 feet (s = 5) with an initial vertical velocity of 30 feet per second (v = 30). Zack catches it at a height of 7 feet (h = 7).

We can rewrite the equation as:

7 = 16t^2 + 30t + 5

To find the time (t) when the flag is at a height of 7 feet, we can rearrange the equation and solve for t. However, since this is a quadratic equation, we can also use the quadratic formula.

The quadratic equation in this case is:

16t^2 + 30t + 5 - 7 = 0

16t^2 + 30t - 2 = 0

Now, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Applying the values from the quadratic equation, we have:

t = (-30 ± √(30^2 - 4 * 16 * (-2))) / (2 * 16)

Simplifying further:

t = (-30 ± √(900 + 128)) / 32

t = (-30 ± √1028) / 32

Using a calculator, we find two solutions:

t ≈ -1.08 seconds or t ≈ 0.06 seconds

Since time cannot be negative in this context, we discard the negative solution.

Therefore, to the nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

The sum of the first 13 terms of the sequence is -67,108,863.

Step-by-step explanation:

Sum of the first n terms of a geometric sequence:

The sum of the first n terms of a geometric sequence, with first term \(a_1\) and ratio r, is given by:

\(S_n = \frac{a_1(1-r^n)}{1-r}\)

In this question:

\(a_1 = -3, r = 4\)

Sum of the first 13 terms:

\(S_{13} = \frac{-3(1 - 4^13)}{1-4} = -67108863\)

The sum of the first 13 terms of the sequence is -67,108,863.

The expression |-4| has a value of 4 when evaluated

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

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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Answer:

1244 DCD

Step-by-step explanation:

Answer:

x = 2.4

Step-by-step explanation:

4x + 5 / x + 7
combine like terms

X + 4x = 5x

5 + 7= 12

12/ 5x

Divide

12 /5= 2.4

X= 2.4

Answer:

  3

Step-by-step explanation:

The number of tubes can be found from an inequality that relates the number of square inches that can be painted to the number of square inches that must be painted.

Let t represent the number of tubes.

  1400t ≥ 3672 . . . . . the number of tubes that will paint at least 3672 in²

  t > 2.623 . . . . . divide by 1400

If only whole numbers of tubes are available, then ...

  3 tubes are needed to paint the ramp.

Answer:

Step-by-step explanation:

 The number of tubes can be found from an inequality that relates the number of square inches that can be painted to the number of square inches that must be painted.

Let t represent the number of tubes.

 1400t ≥ 3672 . . . . . the number of tubes that will paint at least 3672 in²

 t > 2.623 . . . . . divide by 1400

If only whole numbers of tubes a

Answer:

0.39

Step-by-step explanation:

think about it this way, if you take away the decimal it would be 39 and 04. 04 is another way to write 4 and  4 is less than 39. so 0.04 is less than 0.39

Answer:

0.04 > - 0.39

Step-by-step explanation:

0.04 > - 0.39

Answer:

40.56

Step-by-step explanation:

Answer: about 7 cents

Step-by-step explanation:

1.69/24=0.07..

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Cοmparing bοth unit rate, then  12 bοttles fοr $6 is less then οther.

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here accοrding tο the given, we need tο find unit rate.

Unit  rate = Tοtal cοst / Tοtal number οf bοttles

Cost of 18 bottles = $10

Cost of one bottle = \(\frac{10}{18}\) = 0.555= $0.6

Cost of 12 bottles = $6.

Cost of one bottle = \(\frac{6}{12} =\frac{1}{2}=\$0.5\)

Now comparing both unit price , then  12 bottles for $6 is less then other.

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In mathematical logic, the Law of Detachment says that if the following two statements are true:

( 1 ) If p, then q.

( 2 ) p

Then we can derive a third true statement:

( 3 ) q.

In our question, we have

( 1 ) If 0º< A <90º, then A is an acute angle.

( 2 ) The measure of A is 58º.

Then, from the first statement, we can affirm

( 3 ) A is an acute angle.

Answer:

false

Step-by-step explanation:

97+33

=130

88+24

=112

So the answer is false.

Answer:

1000 meters³

Step-by-step explanation:

20 x 10 x 5 = 1000

the units are in meters and you are measuring the volume so the units is meters³

Volume of rectangular prism is 1000 \(m^{3}\)

1000 \(m^{3}\) of water can a bath tub hold.

"A rectangular prism can be defined as a 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid."

Given

Length of a bath tub = 20 m

Width of a bath tub = 10 m

Height of a bath tub = 5 m

Formula to find the volume of the rectangular prism

Volume of the rectangular prism = length × width × height

= 20 × 10 × 5

=200 × 5

V = 1000 \(m^{3}\)

Volume of the rectangular prism = 1000 \(m^{3}\)

Hence, Volume of rectangular prism is 1000 \(m^{3}\)

1000 \(m^{3}\) of water can a bath tub hold.

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Answer:

the answer is 3

Step-by-step explanation:

21 x 3 =7

hope it helps

Answer:

21/7

Step-by-step explanation:

Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3

Answer:

-9

Step-by-step explanation:

Answer:

27 cm³

Step-by-step explanation:

A = 6 a²

V = a³

V=6A3/2

36=6·543/2

36≈27cm³

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The number of hamburgers sold on Saturday is 108

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Given that:

1. The combined total of hamburgers and cheeseburgers is 432.

2. The number of cheeseburgers sold was three times the number of hamburgers sold

Let h and c represent hamburgers and cheeseburgers respectively

1st sentence can be written as:

h + c = 432   .... (1)

2nd sentence can be written as:

c = 3h   .... (2)

Substitute (2) into (1):

h + 3h = 432

4h = 432

h = 432/4 = 108

Therefore, 108 hamburgers were sold on Saturday

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The Linear equation that represents the above situation is given by

x + 3x + 15 = 63

A linear Equation is a Mathematical expression that is used to calculate an unknown number of values or any unknown quantity. Here we use variables to represent the unknown numbers.    

Here given that

Luke and Cade have started running

Luke runs 15 more miles than thrice of that of number of miles Cade runs

Since we don't know the number of miles run by Cade

Let us assume that Cade runs x miles

=> Number of miles run by Cade = x miles

From the given data,

The number of miles run by Luke will be = 3x + 15

=> Number of miles run by Luke and Cade = x + 3x + 15

Given that the total mile run by Luke and Cade =  63 miles  

=> x + 3x + 15 = 63

Therefore,

The Linear equation that represents the above situation is given by  

x + 3x + 15 = 63

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The number of students signing up for neither Math nor Biology is 25.

A set is a collection of well-defined objects.

A subset contains all the elements or a few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Given, 120 students are signing up for classes. 80 of them are signing up for a Math class (M) and 50 of them are signing up for a Biology.

We know N(A∪B) = N(A) + N(B) - N(A∩B).

∴ N(M∪B) = 80 + 50 - 35.

N(M∪B) = 95.

So, the number of students signing up for neither Math nor Biology are

(120 - 95) = 25

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Answer:

Answer btw is 1/4 ;)

Step-by-step explanation:

First step in dividing fractions is to flip the second fraction, aka find the inverse.

\(\frac{1}{3}/\frac{4}{3} \\\frac{1}{3}*\frac{3}{4}\)

All you have to do from here is multiply.

\(\frac{3}{12}=\frac{1}{4}\)

Boom.

Answer:87.5M

Step-by-step explanation:

1 cm=3.5

25*3.5=87.5

25cm=87.5M