Hama is three times as old as David and the sun of their ages is 52. Determine their ages.

Anna uses 120 g of chocolate and 360 grams of margarine to needed to bake biscuits.

We have data as follows; To make 24 biscuits Anna uses following proportion of Ingredients;

80 g sugar

120 ml syrup

200 g oats

120 g margarine

40 g chocolate

Now We can analysis that anna uses 40 g chocolate to make 24 biscuits

So for 120 g of chocolate Anna can bake [tex] \frac{24(120)}{40}  [/tex]

=  24 (3)

= 72 biscuits

∴ Anna can bake 72 biscuits if she uses 120 g of chocolate.

We want to find how many grams of margarine will she need to make 72 biscuits and this can be done as follows;

Ingredients for 24 biscuits require 120 g margarine

∴ For 72 biscuits anna require [tex] \frac{72(120)}{24}  [/tex] g of margarine

= 3 (120)

= 360 g of margarine.

Hence 360 grams of margarine anna needed.

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The time taken by the rock to hit the ground is  3 seconds.

It is given in the question that:-

[tex]t=\frac{\sqrt{h} }{4}[/tex]

Where,

t represents the time (in seconds) taken by the object to reach the ground, and

h represents the height from which the object is falling

We have to find the time taken by a rock to hit the ground after falling from a height of 125 feet.

Using the formula given in the question, we can write,

[tex]t=\frac{\sqrt{125} }{4}=\frac{5\sqrt{5} }{4}[/tex]

We know that,

[tex]\sqrt{5}[/tex] ≈ 2.23

Hence, we can write,

t ≈ (5*2.23)/4 ≈ 2.7875 ≈ 3 seconds (estimated to nearest integer)

Hence, it takes around 3 seconds for the rock to hit the ground after falling from a height of 125 feet.

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The value of x and y for given equation are (2,15) and (12,24).

Using hit and trial method, we can calculate that the values of given equation are (2,15) and (12,24)

The hit and trial approach is used to balance chemical equations by selecting the least whole number coefficient. tally the instances of each ingredient on either side of a reaction. The element with the lowest frequency of recurrence is considered to be balanced.

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actually the number is "x", which oddly enough is the 100%, so we know that 45% of "x" is 99, what is "x" anyway?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 99& 45 \end{array} \implies \cfrac{x}{99}~~=~~\cfrac{100}{45} \\\\\\ \cfrac{x}{99}=\cfrac{20}{9}\implies 9x=1980\implies x=\cfrac{1980}{9}\implies x=220[/tex]

The statements that are true are:

3) m∠JKL = 45°

4) m∠MKQ + m∠PKQ = m∠PKM

5) line PK is an angle bisector

1) This statement says that KQ is an angle bisector. This is false because the line KQ does not pass through the diagonal vertex of the right angled symbol at point K.

2) Second statement says that ∠LKQ is bisected. This statement is false because PK is just a perpendicular line to JKM that divides it into 2 equal parts and not a bisector of ∠LKQ

3) The third statement states that m∠JKL = 45°. This statement is true because from the image it is clear that the line KL divides m∠PKJ into two equal parts.

4) Fourth statement says that m∠MKQ + m∠PKQ = m∠PKM. This statement is true. Now, although KQ doesn't bisect m∠PKM into 2 equal parts, nevertheless it divides it into 2 angles namely m∠MKQ and m∠PKQ. This means the sum of m∠MKQ  + m∠PKQ must yield m∠PKM.

5) The fifth statement says that the line PK is an angle bisector. This statement is true because JKM is a straight angle. Thus as PK is perpendicular to it, it has bisected it into two equal parts.

6) The fifth statement says that ∠JKL ≅ ∠QKM. This statement is false because ∠JKL is a bisected angle which is 45° whereas, ∠QKM is not a bisected angle and thus not equal to 45°.

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Answer: The factors of 12 are 1, 2, 3, 4, 6, and 12

Hope this helps!

Answer:

The factors of 12 are 1, 2, 3, 4, 6 and 12.

Answer:

370000

Step-by-step explanation:

So it would go from 962-1000. So 370000

Given the algebraic expression 3x⁴ - 5x + 2, each of following represents:

An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.

In Mathematics, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.

In conclusion, an exponent is an operation that raises a numerical value or quantity to the power of another and it is generally written as bⁿ.

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m=x1+x2/2 or m=y1+y2/2

hope you understand

0.6004 is standard deviation of equation .

Why is there a standard deviation?

=0.6004$P(120≤X≤153)=0.6004​

The mean is μ=147, and the standard deviation is σ=16.

0.6462−0.0458=0.6004.

Thus, P(120≤X≤153)=0.6004.

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Answer:

107.5 and 72.5

Step-by-step explanation:

The expression that shows the price x of a new car minus à 25% down payment is x - 0.25 = 0.75x

Based on the information given, it should be noted that the information is to simply illustrate find the expression that shows the price x of a new car minus a 25% down payment.

This will be illustrated as:

= x - (25% × x)

= x - 0.25x

= 0.75x

Therefore, the expression is 0.75x.

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An expression which is equivalent to the given expression 18x² +14x + 7 is given by 14x + 18x² + 7.

As given in the question,

Given expression is :

18x² +14x + 7

Simplify all the optional expression to check which one is equivalent to given expression:

a. 7(18x² + 14x)

   = 126x² + 98x

Not equivalent.

b. 14x + 18x²+ 7

Rearrange it

18x²+14x + 7 .

Equivalent.

c. 32x³ + 7

Degree is 3.

Not equivalent.

d. 18x²(14x + 7)

= 252x³ +126x²

Not equivalent.

Therefore, an equivalent expression of 18x²+14x + 7 is 14x + 18x²+ 7.

The complete question is:

Which of the following is an equivalent expression of 18x²+14x + 7?

7(18x² + 14x)

14x + 18x²+ 7

32x³ + 7

18x²(14x + 7)

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Answer: The correct answer is B.

Step-by-step explanation:

To evaluate this expression you must divide x-1 though the expression or factor out the upper half of the equation and cancel out what is necessary.

The division method: attached below :)

Ian is 144 centimeters tall now by solving the equation.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Let Lisa, Ian, and Jim's real heights are L, I, and J, respectively.

Lisa's friend Ian is 4 centimeters taller than her, therefore L=4+I

In the sentence "Ian is 8 cm taller than Jim.": I=8+J, 

Hence, J=I-8 

Thus, Lisa, Ian, and Jim are 4+I, I, and I-8 correspondingly in height.

Since their heights increase by 2 cm every 4 months, this results in an 8-centimeter height increase.

Thus, after four months, Lisa, Ian, and Jim reach the following heights:

4+I+I+8, I+8, and I-8+8 that equal to I+12, I+8, and I respectively

"The total of Ian's and Jim's heights will be 140 centimeters more than Lisa's height in four months" means:

(I + 8) + I = 140 + (I + 12)

⇒2I + 8 = 152+I

⇒I = 144

⇒I=152-8

=144

Therefore, Ian is 144 centimeters tall now.

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Answer:

y = 3x + 19

Step-by-step explanation:

Here m is the slope and b is the y-intercept.

     y = 3x + 4

m = 3

Parallel lines have same slope.

   m = 3

y = 3x + b

Substitute (-5,4) in the above equation.

        4 = 3*(-5) + b

        4 = -15 + b

  4 + 15 = b

           b = 19

Equation of the line: y = 3x + 19

Answer: y = 3x +19

Step-by-step explanation:

-Parallel lines have the same gradient

y = 3x + c

rearrange to give c= y - 3x

substitute x = -5 and y = 4

c = 3 - (3x-5)

c= 19

so the equation is y = 3x + 19

The error is that vertical angles are congruent, and don't necessarily add to 180°. Vertical angles only add to 180° if they are right angles.

[tex]13x+45+19x+3=180 \\ \\ 32x+48=180 \\ \\ 32x=132 \\ \\ x=33/8[/tex]

Answer:

x = 7

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent.

Angles on a Straight Line Theorem

The sum of angles formed on a straight line is equal to 180°.

The error made is confusing the Vertical Angle Theorem with the Angles on a Straight Line Theorem.  To find x, we should either:

Applying the Vertical Angle Theorem:

[tex]\boxed{\begin{aligned} (13x+45)^{\circ} &=(19x+3)^{\circ} \\13x+45&=19x+3\\13x+42&=19x\\42&=6x\\x&=7\end{aligned}}[/tex]

Applying the Angles on a Straight Line Theorem:

[tex]\boxed{\begin{aligned}(6x+2)^{\circ}+(19x+3)^{\circ}&=180^{\circ}\\6x+2+19x+3&=180\\25x+5&=180\\25x&=175\\x&=7\end{aligned}}[/tex]

Therefore, the value of x is [tex]\boxed{x=7}[/tex] .

Answer:

See below:

Explanation:

1.7 dm =  .17 m     assuming  dm is decimeter

.17m  * 10^7  scale  = 1.7 x 10^6 m  = 1.7 x 10^3 km  = 1700 km

The maximum that the company can expect for returned items is C. $5972.65

From the information, the average daily profit of an electronics store is $31,435 and the company estimates that 15% is lost each day to returns, with a margin of error of ±4%.

In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.

The maximum the company can expect for returned items will be:

= (15% + 4%) × Profit

= 19% × $31,435

= 0.19 × $31,435

= $5972.65

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Triangle PUB is divided into 2 triangles that is ΔPUM and ΔPMB. We have angles ∠B=35°,∠U=62°,∠P=21°. The angles are ∠1=56° and ∠2=62°.

Given that,

In picture there is a triangle with the intersection line in between the triangles.

Triangle PUB is divided into 2 triangles that is ΔPUM and ΔPMB.

We have angles

∠B=35°,∠U=62°,∠P=21°

We have to find the angle of angle 1 and 2.

We know,

In triangle sum of the 3 angles is 180°.

Now, we take ΔPMB

We find the other angle of M.

21°+35°+M=180°

M=180°-21°-35°

M=180°-56°

M=124°

So, now we can find the angle 1.

the straight line has a angles of 180°.

124°+∠1=180°

∠1=180°-124°

∠1=56°

Now, we find angle 2.

Take ΔPUM

62°+∠1+∠2=180°

62°+56°+∠2=180°

∠2=180°-62°-56°

∠2=180°-118°

∠2=62°

Therefore, the angles are ∠1=56° and ∠2=62°.

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GROUP LIKE TERMS TOGETHER.

[tex]3x - 1.79x = 1 - 8 \\ 1.21x = - 7 \\ \frac{1.21x}{1.21} = \frac{ - 7}{1.21 \\ } \\ x = 5.7851239669[/tex]

Answer:

x=[tex]\frac{10}{7}[/tex]

Step-by-step explanation:

8 + 3x = 1 + 7.9x

1. multiply everything by 10 so there is no longer a decimal in the equation

80+30x=10+79x

2. get the x on one side so we -10 and 30x from both side

70=49x

3. divide by 49 on each side as we want to find the value of x

[tex]\frac{70}{49}[/tex]=x

4. the fraction can be simplified to

[tex]\frac{10}{7}[/tex]=x

4. the final answer is

[tex]\frac{10}{7}[/tex]=x

Using angle addition postulate when ∠1 ≅ ∠4 it is proved that ∠2 ≅ ∠3.

As given in the question,

Given: ∠1 ≅ ∠4. Prove ∠2 ≅ ∠3.

(Using angle addition postulate)

    Statements                                              Reasons

1. ∠1 ≅ ∠4           Given

2. ∠1 = 180 - ∠2  Being supplementary angles (angle addition postulate)

3. ∠4 = 180 - ∠3  Being supplementary angles (angle addition postulate)

4. 180 - ∠2 = 180 - ∠3      Substituting Statements 2 & 3 into Statement 1.

5. ∠2 = ∠3                        Simplifying Statement 4 algebraically.

In statement 4, the constants 180 cancel out from either of left hand side (LHS) and right hand side (RHS). Thus the equation gets simplified to Statement 5. It is worthwhile to mention that Supplementary angles or linear pair always sum up to 180° in measure. Additionally linear pair form a straight line together.

Therefore, using angle addition postulate when ∠1 ≅ ∠4 it is proved that ∠2 ≅ ∠3.

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Answer: -5j+15

step by step equation

Answer:

[tex]\boxed{a} \quad \boxed{|b - c|} \quad \boxed{|a - b|} \quad \boxed{|a - c|}[/tex]

Step-by-step explanation:

The bars either side of an expression or a value are the absolute value symbol.  "Absolute value" means how far a number is from zero.   Therefore, the absolute value of a number is its positive numerical value.  

The values of a, b and c are negative. All expressions except "a" are absolute values, and are therefore positive numerical values. Therefore, "a" is the least expression.

The simplest way to calculate each expression's numerical value is by assigning approximate numbers to each value, then carrying out each calculation.

From inspection of the graph:

[tex]\begin{aligned} \implies |a - b| & \approx |-3.8 - (-1.3)|\\ & = |-2.5| \\ &= 2.5\end{aligned}[/tex]

[tex]\begin{aligned} \implies |b - c| &\approx |-1.3 - (-0.7)| \\ &= |-0.6| \\ &= 0.6\end{aligned}[/tex]

[tex]\implies a \approx -3.8[/tex]

[tex]\begin{aligned} \implies |a - c| &\approx |-3.8 - (-0.7)| \\ &= |-3.1| \\ &= 3.1\end{aligned}[/tex]

Therefore:  -3.8 < 0.6 < 2.5 < 3.1

Hence, the expressions from least to greatest are:

[tex]\boxed{a} \quad \boxed{|b - c|} \quad \boxed{|a - b|} \quad \boxed{|a - c|}[/tex]

The construction of the angle bisector of [tex] \angle ABC[/tex], gives the completed statement as follows;

An angle bisector is the ray or line, dividing an angle into two congruent angles.

The steps required to construct the angle bisector of [tex] \angle ABC[/tex] is presented as follows;

The complete statement is therefore;

To construct the angle bisector of.[tex] \angle ABC [/tex], first set the point of the compass on B and draw an arc through BA and BC

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