A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams. How much did each sensor weigh originally?

Answer:

49.50

Step-by-step explanation:

8.00 x 4 = 32.00

35 x .50 = 17.50

32.00 + 17.50 = 49.50

Answer:

$12 per pair of glass.

$6 per glass.

Step-by-step explanation:

48/8 = 6

A pair is 2, so I multiplied 6 by 2.

6 x 2 = 12

So, Taryn paired $12 per glass.

--

ANSWER: $12 per pair

EXPLANATION: $48 divided by 8 pairs of glasses equals $6 per glasses. So then you multiply 6 by 2 to get the amount per pair.

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[3] can be expressed as a linear combination of [2] and [0].

To express [3] as a linear combination of [2] and [0], we need to find coefficients (multipliers) that, when multiplied by the vectors [2] and [0], will add up to [3].

Let's assume that the coefficients for [2] and [0] are a and b, respectively. We have the equation a[2] + b[0] = [3].

Since [2] is a scalar multiple of [2], we can rewrite the equation as 2a + 0b = 3.

Simplifying the equation, we get 2a = 3.

Solving for a, we find a = 3/2.

Now, substituting the value of a back into the equation, we have 3/2[2] + b[0] = [3].

Multiplying, we get [3] + b[0] = [3].

Since any multiple of [0] is the zero vector, b[0] is the zero vector.

Therefore, we can express [3] as a linear combination of [2] and [0] by setting a = 3/2 and b = 0.

[3] = (3/2)[2] + 0[0] = [3/2].

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Answer:

Question 858558: a buisness had $10,000 profit in 2000. then the profit increased by 8% each year for the next 10 years. write a function that models the profit in dollars over time Answer by josmiceli(19441) (Show Source):

Excess on the maximum value is commonly known as an overflow error.

An overflow error occurs if a program, video, or similar receives a value that is higher than the maximum value the program or video can handle. This implies the maximum value had been exceeded.

This situation occurs with the video described because due to the number of users that watch the video, the maximum value, which is 32 bits is exceeded.

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Consequently, the graph is correct; and the x values for the solutions are x = -2 and x = 0.

The solution to f(x) = g(x) is the value(s) of x that satisfy the equation. In other words, it is the value(s) of x that make f(x) equal to g(x).

The only problem here is determining which graph is correct:

f(x) is the same on both graphs;

g(x) = 2 |x + 2| is the absolute value graph of lxl stretched vertically two units to the left;

the "vertex" of lxl is (0, 0);

consequently, the first graph is correct; and the x values for the solutions are x = -2 and x = 0.

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Answer:

3x - 11

Step-by-step explanation:

x + 5/ 3x-11

3x - 11 is the quotient

Therefore, the sum of the first 1234 terms of this sequence is 1234.

To find the sum of the first 1234 terms of the sequence consisting of 1's separated by blocks of 2's with n 2's in the nth block, we need to determine the number of blocks and the number of 1's in each block.

Let's examine the pattern of the sequence:

Block 1: 2's

= 1's

= 1 (1 2)

Block 2: 2's

= 2's

= 22 (1 22 1)

Block 3: 2's

= 3's

= 222 (1 222 1)

Block 4: 2's

= 4's

= 2222 (1 2222 1)

...

We observe that the number of 2's in each block is equal to the number of the block itself. So, in the nth block, there are n 2's.

Now, let's calculate the number of blocks required to reach the 1234th term:

To find the number of blocks, we need to determine the maximum block number before the 1234th term. We can calculate this by finding the sum of the series 1 + 2 + 3 + ... + n until the sum is greater than or equal to 1234.

The formula for the sum of the series 1 + 2 + 3 + ... + n is given by: S = (n/2)(n+1).

Let's solve this equation:

(n/2)(n+1) = 1234

\(n^2 + n - 2468 = 0\)

Using the quadratic formula:

n = (-1 + √(1 + 4*2468)) / 2

n ≈ 61.76

Since n must be a whole number, we take the ceiling of n, which gives us 62.

Therefore, there are 62 blocks in the sequence.

Next, let's calculate the number of 1's in each block:

In the nth block, there are n 2's. Since each 2 is separated by a 1, there are n + 1 terms in each block.

So, the number of 1's in each block is (n + 1) - n = 1.

Since there is always one 1 between two consecutive blocks, the total number of 1's in the sequence is equal to the number of blocks, which is 62.

Finally, let's calculate the sum of the first 1234 terms:

Each block has n + 1 terms, which gives us (n + 1) + (n + 1) + ... + (n + 1) (62 times).

Sum of (n + 1) repeated 62 times = 62(n + 1)

= 62 * 2

= 124.

In addition to the blocks, we have 1234 - 62 = 1172 remaining terms, which are all 1's.

So, the sum of the first 1234 terms is 62 + 1172 = 1234.

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Answer:

20x^6

Step-by-step explanation:

20x^6

(5x^3)(4x^3)

The probability of winning a prize worth more than the price of playing the game is 38%.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

Given that the percentage of the winning price is:-

Toy = 25%

Soda = 25%

Candy = 37%

Mega win = 13%

The probability of winning a prize worth more than the price of playing the game is calculated as:-

P = ( 25 + 13 ) x 100 / 100

P = 0.38 x 100

P = 38%

Therefore, the probability will be 38%.

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Answer:

Let B {bı, b2} and C = {c1, c2} be bases for R^2 where bı [-1;8]. b2 [1;-5], c1 = [1;4]. Find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B.

In the given problem, we have the bases B and C as follows:

B = {b1, b2} where b1 = [-1;8] and b2 = [1;-5]

C = {c1, c2} where c1 = [1;4] and c2 = [0;1]

We need to find the change-of-coordinates matrix from B to C and from C to B.

To find the change-of-coordinates matrix from B to C, we need to express the basis vectors of B in terms of the basis vectors of C. We can do this by solving the following equations:

b1 = x1c1 + y1c2

b2 = x2c1 + y2c2

where x1 , y1, x2, and y2 are the coefficients we want to find.

Substituting the given values, we get:

[-1;8] = x1*[1;4] + y1*[0;1]

[1;-5] = x2*[1;4] + y2*[0;1]

Solving these equations, we get:

x1 = -17/4, y1 = 1/4, x2 = 9/4, and y2 = -1/4

Therefore, the change-of-coordinates matrix from B to C is:

[-17/4  9/4]

[ 1/4 -1/4]

To find the change-of-coordinates matrix from C to B, we need to express the basis vectors of C in terms of the basis vectors of B. We can do this by solving the following equations:

c1 = a1b1 + a2b2

c2 = b1b1 + b2b2

where a1 , a2, b1, and b2 are the coefficients we want to find.

Substituting the given values and solving these equations, we get:

a1 = 4/17, a2 = -1/17, b1 = -1/17, and b2 = -5/17

Therefore, the change-of-coordinates matrix from C to B is:

[ 4/17 -1/17]

[-1/17 -5/17]

I hope this helps!

Step-by-step explanation:

Since $14 is the price after a 30% discount then $14 is 70% of the original price.

$14/70=x/100 (100% would be the original price)

1400=70x or 1400/70 = $20!

You can double check the work by taking 30% off the $20 (10% would be $2, 30% would then be $6) 20-6=14!

If the average pain score after hypnotism is lower than the average pain score before hypnotism, it indicates that hypnotism is effective in reducing pain, on average.

To determine if the sensory measurements, on average, are lower after hypnotism, we need to analyze the data from the study. The table showing the results for randomly selected subjects can be used to calculate the mean scores for the group before and after hypnotism. If the mean score is lower after hypnotism, then we can conclude that hypnotism is effective in reducing pain. However, we need to ensure that the sample size is large enough and that the study was conducted properly to minimize any potential biases or confounding factors. Therefore, further investigation may be required before making any conclusive statements about the effectiveness of hypnotism in reducing pain. To investigate the effectiveness of hypnotism in reducing pain, we need to compare the sensory measurements before and after hypnotism. Here's a step-by-step explanation:
1. Obtain the data of randomly selected subjects' pain scores before and after hypnotism.
2. Calculate the average pain score for the subjects before hypnotism.
3. Calculate the average pain score for the subjects after hypnotism.
4. Compare the average pain scores before and after hypnotism.

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Answer:

To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.

So,

(x + 4)² = x² + 2(x)(4) + 4²

= x² + 8x + 16

Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.

Step-by-step explanation:

Answer:

x²n+ 8x + 16

Step-by-step explanation:

(x + 4)²

= (x + 4)(x + 4)

each term in the second factor is multiplied by each term in the first factor, that is

x(x + 4) + 4(x + 4) ← distribute parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16

The missing term in the polynomial is 8x³y² - __ + 3xy² - 4y³ is  x²y².

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, A polynomial 8x³y² - __ + 3xy² - 4y³.

Now, If we observe the terms we can conclude 'x' has decreasing powers and y has increasing powers, therefore, the term could be put in the blank to create a fully simplified polynomial written in standard form is x²y².

So, The polynomial is 8x³y² - x²y² + 3xy² - 4y³.

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I think C would be for number 11

A is for 12.

x/2 < - 18

Answer:

Step-by-step explanation:

2,734 is your answer.

Answer: A . 0

Step-by-step explanation:

The two smaller sides does not equal to the longer length or greater than the longer length so no triangles can be form.

To estimate ∫402 using left endpoints for =5 approximating rectangles, we need to calculate the width and height of each rectangle.

The width of each rectangle is determined by dividing the total interval, in this case, 2, by the number of rectangles, which is 5. Therefore, the width of each rectangle is 2/5 = 0.4.

Next, we need to find the height of each rectangle. Since we are using left endpoints, we evaluate the function at the left endpoint of each rectangle. In this case, the left endpoints are 40, 40.4, 40.8, 41.2, and 41.6.

Now, we calculate the height of each rectangle by evaluating the function, which is 2x, at these left endpoints. The height of each rectangle is: 2(40) = 80, 2(40.4) = 80.8, 2(40.8) = 81.6, 2(41.2) = 82.4, and 2(41.6) = 83.2.

Finally, we multiply the width and height of each rectangle and sum them up to estimate the value of the integral.

The estimate for ∫402 using left endpoints for 5 approximating rectangles is: 0.4(80) + 0.4(80.8) + 0.4(81.6) + 0.4(82.4) + 0.4(83.2) = 329.6.

In conclusion, ∫402 is approximately 329.6 when using left endpoints for 5 approximating rectangles.

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\(\sf\large \green{\underbrace{\red{Answer⋆}}}:\)

[A] Right option is C

[B] 11.55

Step-by-step explanation:

\( \sf \tan A{ \degree} = \frac{Perpendicular}{Base} \)

\( \sf \tan 60{ \degree} = \frac{20}{x} \\ \sf x = \frac{20}{ \tan60{ \degree}} \)

now we need to find value of x

tan 60° = √3

\( \sf x = \frac{20}{ \sqrt{3} } \)

first we need to rationalize by multiplying √3 in numerator and denominator

\( \sf x = \frac{20 \sqrt{3} }{3} \\ \sf x = \frac{34.64}{3} \\ \sf x = 11.55\)

The quadrilateral with no pair of parallel sides is trapezium

Given data ,

A = a quadrilateral with no pair of parallel sides

This type of quadrilateral is called a trapezium. In some countries, a trapezium is defined as having exactly one pair of parallel sides, while in other countries, a trapezium is defined as having at least one pair of parallel sides.

In any case, a quadrilateral with no pair of parallel sides is not considered a trapezium. Instead, it is known as a general quadrilateral.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

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The sales tax for a box of cereal that costs $3.8 is $0.228 and the total cost for this box of cereal at the checkout register is $4.028, given that sales tax is 6% of the price of the item. This can be obtained by using sales tax formula.

The Sales tax formula is given by,

⇒ Sales tax = Total sales × sales tax rate

⇒ Sales tax = item price × 6%  

⇒ Sales tax = 0.06 × item price

Here in the question it is given that,  

a box of cereal costs $3.8, that is, item price = $3.8

By using sales tax formula we get that,

⇒ Sales tax = 0.06 × item price

⇒ Sales tax = 0.06 × $3.8

⇒ Sales tax = $0.228

The total cost for this box of cereal at the checkout register can be obtained using the following formula,

⇒ Total cost = item price + sales tax

⇒ Total cost = $3.8 + $0.228

⇒ Total cost = $4.028

Hence the sales tax for a box of cereal that costs $3.8 is $0.228 and the total cost for this box of cereal at the checkout register is $4.028, given that sales tax is 6% of the price of the item.

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The square root of 59 lies in between the square root of 49 and 64

The square root of 49 = 7

The square root of 64 = 8

Hence, it lies between 7 and 8

Answer:

8x - 4

Step-by-step explanation:

Perimeter is the sun of all side lengths. We know the perimeter and two side lengths, so on order to find the third, we need to subtract the first two lengths from the sum. After subtraction, we get 8x - 4.

Answer:

B

Step-by-step explanation:

Its dominant because its brown hair.

Answer:

a) 70 azulejos

b) 37500 litros

c) 37.5m³

Step-by-step explanation:

A piscina tem 5 m de comprimento, 3 m de largura e 2,5 m de profundidade.

Comprimento = 5m

Largura = 3m

Profundidade (altura) = 2,5 m

Calcular:

a) A quantidade de ladrilhos necessária para cobrir a piscina

Isso é calculado como a área de superfície da votação

A = 2 (wl + hl + hw)

A = 2 × (3 × 5 + 2.5 × 5 +2.5 × 3)

A = 70 m²

Observe que:

1 m² = 1 azulejo

70 m² = 70 azulejos

b) A quantidade de água que pode caber na piscina.

1 m³ = 1000 litres

O volume de uma piscina = Comprimento × Largura × Altura

= 5m × 3m × 2.5m

= 37.5m³

1 m³ = 1000 litros

37.5m³ =

37.5 × 1000 litros

= 37500 litros

c) seu volume em m³

O volume de uma piscina = Comprimento × Largura × Altura

= 5m × 3m × 2.5m

= 37.5m³

Answer:

42 cm

Step-by-step explanation:

the first triangle is 7 times bigger than the second triangle. ( 4 x 7 = 28)

so to find out line EG, you times 6 cm by 7. which is 42

Answer:

2y + 2z

Step-by-step explanation:

-x + 2z + x + 2y

= (-1 + 1)x + 2y + 2z

= 2y + 2z

Hope this helped!

The probability of not drawing a face card from a standard deck of 52 cards can be calculated as follows : We know that a standard deck of 52 cards has four suits (clubs, diamonds, hearts, spades), with each suit having 13 cards, and there are 12 face cards in a deck.

Face cards include kings, queens, and jacks, all of which belong to each suit and aren't numbered cards. Let's take one suit as an example. In a deck of cards, we have three face cards (K, Q, and J) and ten numbered cards (2-10).

There are four suits in a deck, so there are 12 face cards in total. Thus, there are 52-12 = 40 non-face cards in a standard deck of cards.The probability of not drawing a face card from a standard deck of 52 cards can be calculated by dividing the number of non-face cards in the deck (40) by the total number of cards in the deck (52).

The probability of not drawing a face card is, therefore, 40/52. Simplifying this fraction we get 10/13 or 0.7692. Thus, the probability of NOT drawing a face card from a standard deck of 52 cards is 0.7692. I hope this helps.

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