what are the products of these problems: 4.3 x 7.2 0.3 x 24 0.9x1

Answer:

hamburger =282 calories

soda=212 calories

Step-by-step explanation:

2h+5c=1624 ...............×3

3h+2c=1270 ................×2

use eliminate method: multiply the first equation by 3, and second one by 2 to eliminate h first:

6h+15c= 4872

6h+4c=2540

subtract the two equations

6h+15c-6h-4c=4872-2540

11c=2332

c=2332/11

c=212 calories in soda

substitute c in any equation to get h

2h+5c=1624

2h+5(212)=1624

2h=1624-1060

2h=564

h=564/2=282

h=282 calories

check :

2(282)+5(212)=

564+1060=1624

3h+2c=1270

3(282)+2(212)=1270

If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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Answer:

4) 26+4/842-/×375-^×

5)/^9+37+×+454+12

Step-by-step explanation:

The graph of the function f(x) = 4(2/3)^x is added as an attachment

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

f(x)=4⋅(

2

3

​)

x

Express the equation properly

So, we have

f(x) = 4(2/3)^x

The above expression is a an equation of a exponential function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the equation in a graphing tool and attach the display

See attachment for the graph of the function

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Answer:

sin(-pi/2) = -1

Step-by-step explanation:

sin (pi/12) cos((7pi)/12) -cos (pi/12) sin((7pi)/12) = -1

cos(-pi/2) = 0

sin(-pi/2) = -1

cos((2pi)/3) = -1/2

sin((2pi)/3) = (√3)/2

The rule used to simplify the above expression is,

Answer:

yes

Step-by-step explanation:

Answer:

The formation of ∆ is possible .

Step-by-step explanation:

Three sides of triangle are given which are 10 , 7 & 15. And we need to determine whetherwecanmake a triangle with these three sides or not . So we know that ,

" Sum of any two sides of a triangle is Greater

than the third side "

Let ,

Here we will see by three cases. And the formation of triangle will be possible if and only of all the three cases are possible.

So , let's check ,

Case 1:-

→ a + b > c

→ 10 + 7 > 15

→ 17 > 15

Case 2:-

→ b + c > a

→ 7 + 15 > 10

→ 22 > 10

Case 3 :-

→ a + c > b

→ 10 + 15 > 7

→ 25 > 7

Since all the three cases are true Hence formation of ∆ is possible.

Answer:

sd

Step-by-step explanation:

Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

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the regular price is "x", which oddly enough is the 100%.

now, the table is 74% off, so that means the sale price is really 100% - 74% = 26%, so is really 26% of the regular price, and we know that's $202.80.

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 202.80& 26 \end{array} \implies \cfrac{x}{202.80}~~=~~\cfrac{100}{26} \implies \cfrac{x}{202.80}=\cfrac{50}{13} \\\\\\ 13x=(202.80)(50)\implies x=\cfrac{(202.80)(50)}{13}\implies x=780\)

The 11th term of the geometric sequence 1, 4, 16,... is 4¹⁰.

A sequence is a grouping of objects in a particular order that permits repetitions. It has members, just like a set does. The length of the sequence is determined by the number of items.

Consider the geometric sequences 1, 4, 16......

For a geometric sequence a, ar, ar²,.....

Where a is the first term, and r is the common ratio of the sequence.

Then for the sequence 1, 4, 16,...

a = 1 and r = 4

The nth term of a geometric sequence is given as:

aₙ = ar⁽ ⁿ ⁻ ¹⁾

Therefore, the 11th term of the sequence will be:

a₁₁ = 1 × r¹¹ ⁻ ¹

a₁₁ = (4)¹⁰

a₁₁ = 4¹⁰

Hence, the 11th term of the sequence is 4¹⁰.

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Answer:

Step-by-step explanation:

(x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

as the polynomial with rational coefficients that has zeros x=2 and x=3i

(x-2) and (x-3i) are factors of third-degree polynomial.

so ,

⇒(x-2)(x-3i)

solving (x-3i)

x = 3i

squaring both sides,

x² = -9

so , (x²+9) is a factor.

hence , (x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

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~Hello! I will try to help you!

\( \: \Rightarrow\sf \int^{1}_{ - 1} \: (2x + 1)dx = . \: . \: . \\\)

»Our first step is to find the integration (2x + 1), then:-

\( \Rightarrow \sf ( \frac{2}{1 + 1} {x}^{1 + 1} ) + x \: ]^{1}_{ - 1} \\ \Rightarrow \sf( \cancel{\frac{2}{2} } {x}^{2} ) + x \: ]^{1}_{ - 1} = \rm {x}^{2} + x \: ]^{1}_{ - 1}\)

»The next step is to just substitute for the upper limit of 1 and the lower limit of -1 to find the result.

\( \Rightarrow \sf( {1}^{2} + 1) - (( - 1) {}^{2} + ( - 1)) \\ \Rightarrow \sf(1 + 1) - (1 + ( - 1)){}{} \\ \Rightarrow \sf2 - 0 \\ \Rightarrow \bf2\)

With this it's done!

Definite Integration

\(\rightarrow \sf \int\limits^1_{-1} {(2x+1)} \, dx\)

integrate the following

\(\rightarrow \sf { [ \dfrac{2x^2}{2} +x ] }_{-1}^1\)

simplify

\(\rightarrow \sf [x^2+x]_{-1}^1\)

apply limits

\(\rightarrow \sf (1)^2+(1) - ( (-1)^2 +(-1))\)

simplify

\(\rightarrow \sf 2 - 0\)

\(\rightarrow \sf 2\)

Answer:

A. 28

Step-by-step explanation:

x = 28

Value of x in the rhombus is  \(28^{0}\).

A rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides. In addition to this, a rhombus has all four sides equal just like a square.

According to the question

DB, CA are diagonal line

So, <CAB + <DBA = \(90^{0}\)

⇒ x + 6 + 2x =   \(90^{0}\)

⇒ 3x = 90 - 6

⇒ 3x = 84

⇒ x = \(\frac{84}{3}\)

⇒ x = \(28^{0}\)

Hence, value of x in the rhombus is  \(28^{0}\).

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True. Summarizing allows you to focus on the important information by finding the introduction, topic sentence and conclusion.

Summarizing is a technique that helps to distill the main points of a text by identifying the introduction, topic sentence, and conclusion. It involves condensing the information to focus on the most important aspects and omitting unnecessary details.

This process enables the reader to grasp the core message of the text quickly and efficiently.

By summarizing, one can communicate the key ideas in a concise and clear manner, making it easier for others to understand and engage with the information presented.

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Answer:

a) 0.0618 = 6.18% probability that the sample will contain at least three defectives.

b) 0.076 = 7.6% probability that the sample will contain at least three defectives

Step-by-step explanation:

Binomial probability distribution

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

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Normal probability distribution

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

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).

Sample of 20 items is selected from the machine.

This means that \(n = 20\)

5% defectives

This means that \(p = 0.05\)

(a) the normal approximation to the binomial

The mean is:

\(\mu = E(X) = np = 20*0.05 = 1\)

The standard deviation is:

\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.05*0.95} = 0.9747\)

The probability is, using continuity correction, \(P(X \geq 3 - 2.5) = P(X \geq 2.5)\) , which is 1 subtracted by the pvalue of Z when X = 2.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{2.5 - 1}{0.9747}\)

\(Z = 1.54\)

\(Z = 1.54\) has a pvalue of 0.9382

1 - 0.9382 = 0.0618

0.0618 = 6.18% probability that the sample will contain at least three defectives.

(b) the exact binomial tables

This is:

\(P(X \geq 3) = 1 - P(X < 3)\)

In which

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.358\)

\(P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.377\)

\(P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.189\)

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.358 + 0.377 + 0.189 = 0.924\)

\(P(X \geq 3) = 1 - P(X < 3) = 1 - 0.924 = 0.076\)

0.076 = 7.6% probability that the sample will contain at least three defectives

Answer:

a) .38 × 2,450 = 931 people buy the local newspaper.

b) 2,450 - 931 = 1,519 people do not buy the local newspaper.

Answer:

The final answer is 7.

Step-by-step explanation:

Since the question states that Little's law can be applied to any single part of the store (for example, just the checkout line), then the average number of shoppers,

�

, in the checkout line at any time is

�

=

�

�

, where

�

is the number of shoppers entering the checkout line per minute and

�

is the average number of minutes each shopper spends in the checkout line.

Since 84 shoppers per hour make a purchase, 84 shoppers per hour enter the checkout line. However, this needs to be converted to the number of shoppers per minute (in order to be used with

�

=

5

). Since there are 60 minutes in one hour, the rate is

84

shoppers

per

hour

60

minutes

=

1.4

shoppers per minute. Using the given formula with

�

=

1.4

and

�

=

5

yields

�

=

�

�

=

(

1.4

)

(

5

)

=

7

Therefore, the average number of shoppers,

�

, in the checkout line at any time during business hours is 7.

Answer:

BEDMAS

Step-by-step explanation:

first: inside the bracket.

second: exponent

third and fourth :division or multiplication. Wich come first.

last :addition or subtraction. Wich come first .

Answer:

E

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

slope = rise / run = 7 / 1 = 7

m = 7

y-intercept = 0

So:

y = 7x + 0

y = 7x

Answer:

15

Step-by-step explanation:

5x - 6 = 4x + 9

    +6         + 6

    5x = 4x + 15

  -4x     - 4x

x = 15

Answer:

5 feet

Step-by-step explanation:

1 second =-3 inches what of

4 seconds=?

-3×4÷1=-12 inches

-12 inches =-1 foot

6 feet + (-1) foot= 5 feet

Answer:

321489

Step-by-step explanation:

Answer:

Step-by-step explanation:

o prove the first associative law of set theory, we need to show that for any sets A, B, and C:

A ∪ (B ∪ C) = (A ∪ B) ∪ C

To do this, we need to show that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa.

First, let's consider an arbitrary element x.

If x ∈ A ∪ (B ∪ C), then x must be in A, or in B, or in C (or in two or more of these sets).

If x ∈ A, then x ∈ A ∪ B, and so x ∈ (A ∪ B) ∪ C.

If x ∈ B, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.

If x ∈ C, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.

Therefore, we have shown that if x ∈ A ∪ (B ∪ C), then x ∈ (A ∪ B) ∪ C.

Next, let's consider an arbitrary element y.

If y ∈ (A ∪ B) ∪ C, then y must be in A, or in B, or in C (or in two or more of these sets).

If y ∈ A, then y ∈ A ∪ (B ∪ C), and so y ∈ (A ∪ B) ∪ C.

If y ∈ B, then y ∈ A ∪ B, and so y ∈ A ∪ (B ∪ C), which means that y ∈ (A ∪ B) ∪ C.

If y ∈ C, then y ∈ (A ∪ B) ∪ C.

Therefore, we have shown that if y ∈ (A ∪ B) ∪ C, then y ∈ A ∪ (B ∪ C).

Since we have shown that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa, we can conclude that:

A ∪ (B ∪ C) = (A ∪ B) ∪ C

This proves the first associative law of set theory.

Answer:

Step-by-step explanation:

I assume that you mean cos(x)/x, not cos(x/x).

Use the quotient rule.