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1 month ago

10

A charity bingo game costs $2 per round and has a $13 entry fee for an adult. It costs $3 per round and a $10 entry fee for a ch

ild. For how many rounds of bingo are the costs the same for an adult and a child?
a 2
b 3
c 4
d 5

2 answers:

AnnZ [12.3K]1 month ago

4 0

En este problema definimos:

x: cantidad de rondas para adultos

y: cantidad de rondas para niños

Queremos conocer para cuántas rondas el costo de jugar bingo es igual para adultos y niños.

Costo adulto = 2x + 13

Costo niño = 3y + 10

Igualando:

$2x + 13 = 3y + 10$

Buscamos que el número de rondas sea igual, es decir, x = y:

$2x + 13 = 3x + 10\\2x-3x = 10-13\\-x = -3\\x = 3$

Con esto, comprobamos que a las 3 rondas ambos costos coinciden.

Respuesta:

3

Zina [12.3K]1 month ago

3 0

Respuesta:

b. 3

Explicación paso a paso:

Formamos dos ecuaciones, una para adultos y otra para niños:

Sea x la cantidad de rondas.

Adulto (A):

A = 2x + 13

Niño (C):

C = 3x + 10

La pregunta es: ¿para qué valor de x son iguales A y C? Por lo tanto, resolvemos:

A = C

2x + 13 = 3x + 10 restamos 10 en ambos lados

2x + 3 = 3x

Restamos 2x:

3 = x

Por ende, la cantidad de rondas es 3.

Verificación:

A = 2x + 13 C = 3x + 10

= 2(3) + 13 = 3(3) + 10

= 6 + 13 = 9 + 10

= 19 dólares = 19 dólares

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PIT_PIT [12445]

Answer:

172.7 sqft (square feet)

Step-by-step explanation:

SA = 2(pi)(r)(h) + 2(pi)r^2

Insert the radius and height to derive SA, then multiply by 10 for the total number of fenceposts.

SA= 2(3.14)(.5)(6)

Calculate

SA=14.39166

Then multiply by 12

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Hope this helps!

5 0

1 month ago

Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o

Svet_ta [12734]

For $\fbox{\begin \\\math{x}=6\\\end{minispace}}$ the function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ both yield the same result.

Detailed breakdown:

The functions involved are

$f(x)=-x^{2}+4x+12$

$g(x)=-x+6$

Step 1:

Insert $x=1$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(1)$ .

$f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15$

Insert $x=1$ in $g(x)=-x+6$ to find the value of $g(1)$ .

$g(1)=-1+6\\g(1)=5$

Step 2:

Insert $x=2$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(2)$ .

$f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16$

Substitute $x=2$ into $g(x)=-x+6$ to find the value of $g(2)$ .

$g(2)=-2+6\\g(2)=4$

Step 3:

Replace $x=3$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(3)$ .

$f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15$

Also, replace $x=3$ in $g(x)=-x+6$ to find the value of $g(3)$ .

$g(3)=-3+6\\g(3)=3$

Step 4:

Insert $x=4$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(4)$ .

$f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12$

Also, replace $x=4$ in $g(x)=-x+6$ to obtain the value of $g(4)$ .

$g(4)=-4+6\\g(4)=2$

Step 5:

Insert $x=5$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(5)$ .

$f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7$

Replace $x=5$ in $g(x)=-x+6$ to find the value of $g(5)$ .

$g(5)=-5+6\\g(5)=1$

Step 6:

Insert $x=6$ into $f(x)=-x^{2} +4x+12$ to find the value of $f(6)$ .

$f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0$

Also, substitute $x=6$ in $g(x)=-x+6$ to obtain the value of $g(6)$ .

$g(6)=-6+6\\g(6)=0$

Step 7:

According to the provided condition $f(x)=g(x)$ .

(a). Insert $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ into the previously mentioned equation.

$-x^{2} +4x+12=-x+6$

(b). Multiply through by $-1$ on both sides.

$x^{2} -4x-12=x-6$

(c). Move the term $x-6$ to the left side of the equation.

$x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0$

(d). Divide the middle term so that its sum equals 5 and the product equals 6.

$x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1,6$

From the analysis above, it is noted that for $x=6$ both functions $f(x)$ and $g(x)$ yield the same outcome.

Using a direct approach:

$f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1$

The table representing function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ is included below.

For more information:

1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)

2. Which is the graph of f(x) = (x – 1)(x + 4)?

6 0

12 days ago

Given: mAngleEDF = 120°; mAngleADB = (3x)°; mAngleBDC = (2x)° Prove: x = 24 3 lines are shown. A line with points E, D, C inters

zzz [12365]

Answer:

" Vertical angles are equal " ⇒ 2nd answer

Step-by-step explanation:

* Refer to the attached illustration

- Three lines intersect at point D.

- We have to identify the missing justification in step 3.

∵ Line FA intersects line EC at point D.

- When two lines cross, the angles created are referred to as

vertical angles.

- By the vertical angles theorem, vertical angles are equal.

Thus, ∠ADC and ∠FDE are vertical angles.

Since vertical angles are equal

∴ ∠EDF ≅ ∠ADC

Thus, m∠EDF ≅ m∠ADC

Given that m∠EDF = 120°.

∵ m∠ADC is the sum of m∠ADB and m∠BDC.

Therefore, m∠ADB + m∠BDC = 120°.

∵ m∠ADB = (3x)° ⇒ given.

∵ m∠BDC = (2x)° ⇒ given.

Thus, 3x + 2x = 120 ⇒ combine like terms.

Thus, 5x = 120 ⇒ divide both sides by 5.

Thus, x = 24.

Column (1) Column (2)

m∠EDF = 120° given

m∠ADB = 3 x given

m∠BDC = 2 x given

∠EDF and ∠ADC are vertical angles definition of vertical angles

∠EDF is equal to ∠ADC vertical angles are equal

equal

m∠ADC = m∠ADB + m∠BDC angle addition principle.

m∠EDF = m∠ADC definition of equality.

m∠EDF = m∠ADB + m∠BDC substitution.

120° = 3 x + 2 x substitution.

120 = 5 x addition.

x = 24 division.

∴ The missing justification is " vertical angles are equal "

- From the reasoning above, ∠ADC and ∠FDE are vertical angles and therefore they are equal according to the vertical angle theorem.

6 0

1 month ago

Read 2 more answers

A dolphin is trying to jump through a hoop that is fixed at height of 3.5m above the surface of her pool. the dolphin leaves the

zzz [12365]

A 40-degree angle may be applicable for this question

4 0

24 days ago

The idle time for taxi drivers in a day are normally distributed with an unknown population mean and standard deviation. If a ra

Svet_ta [12734]

Answer:

$172-2.51\frac{16}{\sqrt{23}}=163.626$

$172+2.51\frac{16}{\sqrt{23}}=180.374$

Hence, in this case, the 98% confidence interval would be (163.626;180.374)

Step-by-step breakdown:

Previous concepts

A confidence interval represents a range that is likely to encompass a population value within a specific confidence level, typically expressed as a percentage whereby a population mean falls between an upper and lower limit.

The margin of errorindicates the span of values surrounding the sample statistic in a confidence interval.

A normal distributionillustrates a probability distribution that is symmetrical around the mean, signifying that values near the mean occur more frequently than those farther away from it.

$\bar X=172$ denote the sample mean

$\mu$ population mean (the variable of interest)

s=16 signifies the sample standard deviation

n=23 represents the sample size

The solution to the query

The equation for the confidence interval of the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

To determine the critical value $t_{\alpha/2}$ , we first need to calculate the degrees of freedom, which is expressed as:

$df=n-1=23-1=22$

Since the confidence level is 0.98 or 98%, we find the value of $\alpha=0.02$ and $\alpha/2 =0.01$ using tools like Excel or a calculator, where the Excel command would be: "=-T.INV(0.01,22)". This yields $t_{\alpha/2}=2.51$

Having all components ready, we can substitute into formula (1):

$172-2.51\frac{16}{\sqrt{23}}=163.626$

$172+2.51\frac{16}{\sqrt{23}}=180.374$

Thus, for this case, the 98% confidence interval will be (163.626;180.374)

3 0

4 days ago